The women, who were dual American-Israeli citizens, were released to the International Committee of the Red Cross and then handed over to the Israel Defense Forces, who took them to be reunited with family at an Israeli military base, the Israeli Foreign Ministry said in a statement.

“Israel, the I.D.F. and the entire security establishment will continue to operate with the best of their abilities and efforts in order to locate all of the missing and return all of the abductees home,” the statement said.

The U.S. government has said that at least 11 other Americans remained unaccounted for after the Hamas terrorist attack on Oct. 7, but it was not clear how many were being held hostage.

President Biden said on Friday that the United States had worked with Qatar to secure the release of Judith and Natalie Raanan. He asked the public to respect their privacy “as they recover and heal.”

“We will not stop until we get their loved ones home,” Mr. Biden said. “I have no higher priority than the safety of Americans held hostage around the world.”

Ms. Raanan and her daughter went to Israel last month to celebrate the Jewish holidays and the 85th birthday of Judith’s mother at a kibbutz in the south of the country.

Judith Raanan spent her early life in Israel before settling in the Chicago suburb of Evanston, Ill., where she raised a family. Natalie Raanan graduated from a public high school in Deerfield, Ill.

On Friday, Rivka Benyihoun, another friend from Chicago, said she and her husband had been watching Israeli television for news of their friend.

“We are all embracing and crying together,” Ms. Benyihoun said. “I told my husband, ‘She’s a survivor. She’s going to make it.’”

In a statement, Gov. J.B. Pritzker of Illinois said he was “incredibly relieved” that the Raanans were safe.

“I cannot wait to welcome them back home after demonstrating immense strength and bravery in the face of unthinkable terror,” Mr. Pritzker said.

The situation of the more than 200 other hostages remains unclear. Israel has not publicly identified them, but military officials have said they include older people and children.

Most were captured from small Israeli towns near the border with Gaza; others were abducted from military bases or from an all-night music festival. They include civilians, soldiers, peace activists, grandparents and a 9-month-old baby.

On Friday, Daniel Hagari, the Israeli military spokesman, disputed Hamas’s claim that it released the Raanans for humanitarian reasons. “This is actually a murderous terrorist organization that right now holds babies, children, women, and elderly people hostage in the Gaza Strip,” he told reporters.

Hostage-taking is a tactic that Hamas has used in the past against Israel.

In 2006, the group seized an Israel soldier, Gilad Shalit, and held him in Gaza for five years. He was exchanged for more than 1,000 Palestinian prisoners, many of whom had been convicted of killing Israelis in terrorist attacks.

The group has also been holding two Israeli civilians who entered Gaza in 2014 on foot, as well as the remains of two Israeli soldiers killed during a war that year.

Shortly after the Oct. 7 attack, Hamas released video of a woman and two small children it said it had released at the Gaza border. But the woman, Avital Aladjem, told Israeli news media that she and the children escaped shortly after crossing the border because their captors left them briefly alone. She said the children belonged to her neighbor, who was killed in the attack.

Earlier this week, Hamas released a short video of Mia Schem, 21, who was abducted during the Hamas assault on the music festival. In the video, she is shown with a bandaged arm and says that she has received medical treatment while in captivity. It is so far the only video the group has released of any of the hostages.

“At the moment I am in Gaza,” Ms. Schem says in the video, which was posted to Telegram channels affiliated with Hamas. “I just ask that I am returned as fast as possible to my family, to my parents, and to my siblings. Please get us out of here as quickly as possible.”

Aaron Boxerman and Julie Bosman contributed reporting

In a statement, a spokeswoman for Web Summit declined to discuss the withdrawals, saying only, “We are looking forward to welcoming 70,000 attendees from around the world with a full program this November.”

The pullout by the two tech giants is the latest blow to Web Summit after its founder and chief executive, Paddy Cosgrave, criticized Western leaders and governments for supporting Israel as it responded to the Hamas raids on Oct. 7. “War crimes are war crimes even when committed by allies, and should be called out for what they are,” he wrote on X on Oct. 13.

Mr. Cosgrave’s comments drew rebuke from prominent technology founders and investors, particularly those from Israel. Among those to drop out were Ravi Gupta, a partner at Sequoia Capital, and Garry Tan, the chief executive of the technology incubator Y Combinator.

Earlier this week, Mr. Cosgrave alternately struck both apologetic and defensive tones, condemning the Hamas attacks but also repeating his criticism of Israel’s military campaign. But by Tuesday, he published an apology on Web Summit’s site in which he said he defended “Israel’s right to exist and to defend itself.” Shortly after, he posted on X that he was taking a break from the social network.

Israeli authorities have yet to formally lay out their plans for a ground invasion. But officials have consistently indicated that one is in the works, and most analysts suggest Israel has little other way of fulfilling its goals against Hamas.

A trip across Israel’s roadways reveals a nation on war footing: clusters of reservists in olive-green uniforms drinking coffee at gas stations and army jeeps zipping down major highways. In border towns close to Gaza, troops can be seen milling about or conducting training as they wait for the war’s next stage to unfold.

Lt. Col. Richard Hecht, the Israeli military spokesman, declined to comment on Friday about when and how Israel’s ground operation would begin. But the Israeli military’s chief of staff, Herzi Halevi, told soldiers on Sunday that their responsibility would be “to enter Gaza,” vowing the troops would attack the places from which Hamas launched its attacks.

Mr. Gallant told lawmakers on Friday that Israel’s campaign against Hamas in Gaza would have three stages: a military campaign of strikes and maneuvering to take out Hamas’s offensive capabilities, then a protracted series of operations to mop up “pockets of resistance” and eventually the establishment of a “new security regime” in Gaza.

Such a campaign “will not take a day, nor a week, and unfortunately, not a month,” Mr. Gallant said, adding that even the first stage would not be easy.

An extended campaign in the Gaza Strip — a coastal enclave populated by more than 2 million people — could lead to heavy casualties on both sides, military analysts said.

The expected ground invasion could see Israeli troops and Palestinian forces engage in deadly close combat in the winding alleys and residential neighborhoods in the north. Hamas militants also have built an extensive network of tunnels under the Gaza Strip, former Israeli officials said, leaving Israeli units with the unusual challenge of how to track and fight commanders and gunmen with the ability to move about under their feet.

Western governments sought to quickly evacuate their citizens from Gaza as the violence intensified ahead of the anticipated ground operation. But diplomatic efforts to enable them to leave Gaza via the Rafah crossing with Egypt have stalled.

After President Biden’s brief trip to Israel this week, Israeli authorities agreed in principle to allow some humanitarian aid into Gaza provided there were checks and that it did not go to Hamas. But trucks loaded with supplies remain on the Egyptian side of the border, and a wide-scale Israeli incursion into the Gaza Strip would complicate any efforts to move and distribute it.

Videos and images from the scene showed rescuers digging through rubble, working with flashlights late Thursday and into Friday. The chapel was not struck.

The Gazan health ministry, which is controlled by Hamas, said at least 16 people were killed and many others were still buried under rubble. The death toll could not be independently confirmed.

A statement from the Israeli military on Friday said that the church was not the intended target of the airstrike. The fighter jets that carried out the attack were trying to destroy a Hamas command center near the church that the military believes has been involved in launching rockets and mortars toward Israel, the statement said.

“As a result of the I.D.F. strike, a wall of a church in the area of the center was damaged,” the statement said, using the initials of the Israel Defense Forces. “We are aware of reports on casualties. The incident is under review. The I.D.F. can unequivocally state that the church was not the target of the strike.”

The church is a five-minute walk from the Ahli Arab Hospital, where an explosion on Tuesday night killed and injured hundreds of people. Hamas blamed the hospital explosion on an Israeli airstrike; Israel has countered that it was caused by a malfunctioning rocket fired by Palestinian Islamic Jihad.

The Israeli military also said on Thursday that it had conducted dozens of strikes against Hamas targets in the Shajaiye neighborhood near the church, calling the area “a terrorist hotbed.” The centuries-old church is in an adjacent neighborhood.

The Orthodox Patriarchate of Jerusalem condemned the airstrike as a war crime.

“The Patriarchate emphasizes that targeting churches and their institutions, along with the shelters they provide to protect innocent citizens, especially children and women who have lost their homes due to Israeli airstrikes on residential areas over the past 13 days, constitutes a war crime that cannot be ignored,” the church said in a statement.

Greece’s Foreign Ministry expressed “deep sorrow” over the strike. “The protection of civilians and the security of places of worship and religious institutions must be safeguarded and respected by all sides,” the ministry said in a statement.

Ainara Tiefenthäler, Iyad Abuheweila and Niki Kitsantonis contributed reporting.

International observers

Israel wants some direct involvement in scrutinizing the cargo that enters Gaza, to ensure that trucks are not carrying weapons. The international community is pressing instead to give trained United Nations staff this task, replicating the model used for aid delivery in Syria.

The United Nations generally prefers that inspections be in the hands of neutral parties so that it cannot be politicized.

Patrick Kingsley contributed reporting from Jerusalem.

Also included in the request are billions of dollars to bolster security along the U.S.-Mexico border, security aid for Taiwan and a fund for humanitarian assistance in hot spots around the world.

The legislative gamble is playing out against a global split screen: wars are raging in Europe and the Middle East, while in the United States, the House has been in a state of chaos for more than two weeks as Republicans struggle to select a speaker.

Mr. Biden’s effort to convince a fractured Congress to back his funding request will test the argument he made to the American people in a speech to the nation Thursday night, when he pressed for global engagement in a deeply unstable world. In that address, he said that the cost to the United States of refusing to invest in that engagement will be high.

“These conflicts can seem far away,” Jake Sullivan, the president’s national security adviser, said in a call with reporters on Friday, as the president’s request was sent to Congress. “But the outcome of these fights for democracy against terrorism and tyranny are vital to the safety and security of the American people.”

Administration officials expressed confidence that there is broad, bipartisan support in both chambers of Congress that should come together quickly to pass the president’s emergency spending proposal.

But the initial reaction on Capitol Hill included some angry words from Republicans, who accused the president of trying to force them into voting for a Ukraine war effort they don’t believe in.

“It’s ridiculous that they’re even trying to lump them together. It’s absolutely outrageous,” said Representative Anna Paulina Luna, Republican of Florida, one of many hard-right G.O.P. members who have urged swift passage of a bill to help arm Israel but have consistently voted against military assistance for Ukraine.

For months, right-wing Republicans have been arguing that programs to arm Ukrainian fighters are siphoning money away from other domestic security objectives and pitching the United States closer to a head-on confrontation with Russia. They have taken a very different tone, however, when it comes to arming Israel in its fight with Hamas, characterizing that as a matter vital to international security.

Even some House Republicans who have continued to support Ukraine assistance took issue with the White House’s approach, and warned that the G.O.P. leadership there would try to split up the package.

“The House should split it up,” Representative Darrell Issa, Republican of California and a regular backer of Ukraine assistance, said of the president’s proposal, adding: “To bring the two together is inherently divisive.”

Last month, more than half of Republicans in the House voted against a bill to replenish a $300 million account dedicated to training and equipping Ukrainian fighters, after several joined hard-liners like Ms. Luna to try to force the administration to be more forthcoming with a plan for victory. Some of those members said that Mr. Biden’s White House speech Thursday night had done little to address their concerns.

“What I want to see is a commander in chief that can sit in the Oval Office and tell America, ‘Here’s what we’re going to do, here’s what we want to spend that money on and here’s what we want our result to be,’ ” said Representative Brad Wenstrup, Republican of Ohio. He said he wanted to see the various security crises covered under Mr. Biden’s request for funds handled separately, in order to get those answers on aid to Ukraine.

If Congress approves Mr. Biden’s combined approach, Ukraine would receive $61.4 billion for military and economic assistance, while Israel would get about $14.3 billion to bolster its air and missile defenses, including the Iron Dome system, which has protected the country from incoming Hamas rockets.

The request also includes more than $9 billion for humanitarian assistance in Israel, Gaza and Ukraine and $7.4 billion for security to support Taiwan and other allies in the Indo-Pacific. It also includes almost $14 billion to fortify border security operations in the United States — a nod to Republican demands that domestic security be considered alongside global conflicts.

Shalanda Young, the director of the Office of Management and Budget, said some of the administration’s request for humanitarian aid would be used to help victims of the violence in Israel and Gaza.

“You’ve already seen a commitment from this administration in making sure humanitarian aid gets to those in Gaza,” she said. “That aid will continue robustly as Congress funds more humanitarian aid.”

Mr. Biden’s allies in the House leadership backed the president’s approach on Friday, predicting that the strategy would prove successful in the end.

“There’s support for it,” said Representative Adam Smith, Democrat of Washington and the ranking member of the Armed Services Committee.

The proposal has already drawn some opposition from the left wing of the Democratic Party, where more than a dozen members have called for a cease-fire in the Israel-Hamas war. They argue that billions in military assistance for Israel would simply accelerate a conflict they are trying to bring to an end.

“Sending more money for weapons doesn’t get us to peace,” Representative Delia Ramirez, Democrat of Illinois, said in an interview.

Ms. Ramirez sounded wary about the money marked for security along the U.S. border with Mexico, saying “more money for enforcement at the expense of immigrants is unacceptable to me.”

The proposal includes about $13.6 billion for additional border patrol agents, immigration judges and other border security measures.

The way the House handles the president’s request may depend in part on how — or whether — Republicans can bring an end to their impasse over choosing a new speaker.

Legislative activity has been at a standstill since a handful of hard-line Republicans orchestrated the ouster of Representative Kevin McCarthy, Republican of California, from the post two and a half weeks ago. No spending package, regardless of its scope, is likely to get a vote until either a replacement is named or members vote to give Representative Patrick McHenry, Republican of North Carolina and the current acting speaker, the power to put bills on the floor.

In the meantime, Senator Chuck Schumer of New York, the Democratic leader, has pledged that the Senate will vote swiftly on Mr. Biden’s full national security package. That could put pressure on the House to follow suit, though the Senate’s appropriations panel is not expected to begin working on legislation to fund the president’s request until the end of the month.

“The Biden administration’s request sends a clear message to America’s friends and allies that we have your back,” he said.

Senator Mitch McConnell of Kentucky, the top Republican in the Senate, also signaled his support for combining the foreign aid requests.

“This is all interconnected,” he told reporters earlier this week.

But even in the Senate, there is some opposition. Senator Tom Cotton, Republican of Arkansas and a frequent critic of the president, issued a blistering statement.

“President Biden’s slush fund proposal is dead on arrival, just like his budgets,” he said, claiming that Mr. Biden’s proposed funding for humanitarian needs in Gaza and elsewhere would help finance Hamas terrorists. “Senate Republicans will take the lead on crafting a funding bill that protects Americans and their interests.”

Palestinian health authorities said that 13 Palestinians, including five children, were killed in the clashes in Nur Shams. The Israeli military reported that one of its officers was killed. Israel also carried out a rare drone strike during the raid, saying that it had attacked “an armed terrorist squad that endangered our forces.”

The Nur Shams refugee camp was not the only hot spot. Since the devastating attack on Israel on Oct. 7 and Israel’s retaliatory strikes on Gaza, Palestinians have been protesting in many towns in the West Bank and clashing with Israeli soldiers.

On Thursday, Israeli forces staged simultaneous raids in Bethlehem, Hebron, Jericho, Nablus and Ramallah, searching for militants connected to Hamas, the armed Palestinian organization that carried out the Oct. 7 attack, which killed more than 1,400 people, mostly civilians.

Since then, Palestinian human rights groups say that more than 70 Palestinians have been killed in the West Bank in clashes with Israeli forces and armed Israeli settlers, by far the most in any consecutive two weeks this year. Israeli officers have arrested hundreds of people, according to Palestinian and Israeli accounts; the Israeli military said on Friday that more than 375 people of those arrested are members of Hamas.

Television news footage broadcast on Thursday showed Israeli Army trucks chugging into Palestinian residential areas and soldiers running across alleyways under the cover of darkness.

Palestinian medics said that Israeli soldiers were blocking them from getting to wounded people. Arab news channels reported that some of wounded had died from loss of blood. Israeli officials could not be immediately reached for comment on the allegation.

United Nations officials said that they were increasingly concerned about the spiraling violence.

“We are extremely alarmed by the rapidly deteriorating human rights situation in the occupied West Bank and the increase in unlawful use of lethal force,” said Ravina Shamdasani, a spokeswoman for the U.N. human rights chief, Volker Türk.

She also said that tighter restrictions on the movement of Palestinians in the West Bank had prevented some from gaining access to health care services for critical conditions.

Aaron Boxerman and Nick Cumming-Bruce contributed reporting.

In recent weeks, Ukrainian officials had expressed growing fears that support for Kyiv was waning as the attention of key allies turned to the war in Gaza; U.S. military aid was bogged down in the Republican struggle for leadership in Congress; and cracks appeared in the commitment of some European countries.

But those concerns were alleviated, at least in part, by Mr. Biden’s argument that continuing to support Ukraine, while simultaneously increasing U.S. military aid to Israel, was in the interests of global stability and American national security.

“We’re not withdrawing,” Mr. Biden said in linking the conflict in Ukraine with the new one in the Middle East. He is expected to request that Congress approve $60 billion in additional assistance to Ukraine and $14 billion more for Israel as part of a joint aid package, though the fate of the assistance could depend on resolving the gridlock that has paralyzed the House of Representatives.

Mr. Biden’s argument for combined support for Israel and Ukraine seemed to echo Mr. Zelensky’s argument that Hamas’s attack on Israel and Russia’s full-scale invasion of Ukraine were both acts of terrorism that called for a similar response.

Mr. Zelensky has also tried to tie Moscow to the Gaza war, portraying it as a malevolent player in the Middle East that supports countries like Iran, which backs Hamas, in an apparent effort to show that defeating Russia would also serve Washington’s interests in the Middle East.

“The world, particularly nations confronting aggression and terrorism, looks to America to lead in preserving our common freedom,” Mr. Zelensky said. “America’s investment in Ukraine’s defense will ensure long-term security for all of Europe and the world.”

Mr. Zelensky’s enthusiastic reception of Mr. Biden’s address is part of a broader shift in tone and approach for the Ukrainian leader, after criticism in the summer that he appeared ungrateful to his allies as he pressed them for more weapons.

In more recent exchanges with Western leaders, including during a trip to the United States last month, Mr. Zelensky has peppered his public statements with expressions of gratitude.

The outlook for the Palestinian economy was already dire before Israel declared a siege of Gaza in retaliation for the Oct. 7 attacks, creating what the World Health Organization called a “humanitarian catastrophe.” An assessment this year by the International Monetary Fund said Israel’s blockade of the Gaza Strip and increased restrictions on the West Bank were significant obstacles to growth and private sector development.

In Israel, as many as 360,000 reservists are leaving their jobs and businesses to mobilize for military duty, bringing parts of the economy to a standstill. Israel’s technology industry, a driver of growth, has abruptly slowed. Production at a major Israeli offshore natural gas field has been shut down. The central bank has committed billions of dollars to prevent Israel’s currency, the shekel, from collapsing.

The conflagration caps a troubling period for an economy that had been riding high, ranked by The Economist last year as the fourth-best-performing economy among the countries in the Organization for Economic Cooperation and Development. Israel’s start-ups have attracted billions in foreign investment. The Abraham Accords, which were signed in 2020 and established diplomatic relations between Israel and several Arab countries, opened a path toward more economic prosperity. Israel is also developing a hub for exporting natural gas to Europe and beyond.

But the economy started to stumble this year after a right-wing government, led by Prime Minister Benjamin Netanyahu, advanced a contentious plan to rein in the power of the judiciary that critics said could potentially weaken the rule of law, inciting millions of Israelis to protest in the streets. Many tech leaders have threatened to leave the country over the judicial overhaul, saying it would undermine Israel’s standing, and warned of an economic downdraft.

The overhaul set off a 60 percent plunge in foreign investment in Israel, and it has hastened an erosion in the shekel’s value and wide swings in the Israeli stock market. High interest rates, rising inflation and expectations of a slowdown in the global economy were also weighing on growth.

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The government’s zeal in pursuit of judicial change generated uncertainty among investors, and “caused money to move out,” said Dan Ben-David, the founder of the Shoresh Institution for Socioeconomic Research and a professor at Tel Aviv University.

“Going into this, we already had an economic problem,” he said. “And then came the Hamas attack.”

Aggravating the shock, Mr. Ben-David added, is that many of the reservists being called to serve in the military are tech entrepreneurs, teachers, lawyers and other secular Israelis, while ultra-Orthodox men are excused for religious reasons. That has concentrated the pool of recruits around people who make up the bulk of Israel’s entrepreneurial economic activity.

Two credit ratings agencies this week warned that Israel’s debt could be downgraded. On Friday Moody’s said that the conflict was “more severe than the episodes of violence in the last few decades,” creating the risk of a diversion of resources in the economy, decreased investment and a loss of confidence.

And the Fitch ratings agency warned on Tuesday of the “heightened risk of a widening of Israel’s current conflict to include large-scale military confrontations with multiple actors, over a sustained period of time.” Just six months ago, Fitch cited Israel’s “strong economic growth.” A ratings downgrade could force Israel to pay higher interest when it borrows.

Goldman Sachs said in a note Monday that the risks to Israel’s financial and economic stability appeared to be lower, for now, than during previous major conflicts because Israel’s overall finances were stronger today and the country had a large stock of foreign exchange reserves.

The Bank of Israel has about $200 billion in foreign exchange reserves — close to 40 percent of the country’s gross domestic product — which its governor, Amir Yaron, told I.M.F. and World Bank officials in a video call on Sunday provided ample capacity to support the economy. Since the conflict, the central bank has earmarked $30 billion in foreign exchange to support the shekel, which has fallen to an eight-year low.

The central bank is facing a quandary: Reduce interest rates to help bolster the wartime economy, or keep them elevated to support the shekel. The bank is scheduled to announce its decision on Monday.

Any war is likely to affect Israel’s finances, Mr. Yaron said, but the government could make budget adjustments to adapt to the conflict. Israel regularly spends over 4 percent of gross domestic product on the military — amounting to $23.4 billion last year — and receives an additional cushion in the form of $3.8 billion in annual aid from the United States, used mainly to buy American weapons. In the coming days President Biden is expected to ask Congress for $14 billion in military and security aid for Israel.

Goldman told clients in its note that it expected Israeli financial authorities to “remain cautious due to potential risks for the conflict to escalate further.”

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The economic situation for Palestinians on the Gaza Strip and in the West Bank has been notoriously worse.

An annual I.M.F. review in August described the heavy toll to the Palestinian economy and people from persistent poverty and high unemployment. The outlook remained “bleak amid a volatile political and security situation,” the I.M.F. concluded, adding that any turnaround would hinge on the “easing of Israeli-imposed restrictions on movement, access and investment,” as well as a political peace settlement.

Israel’s siege of Gaza after the Oct. 7 Hamas attacks has destroyed infrastructure and led to dire shortages of food, water, gasoline and other essentials, and the displacement of about half of Gaza’s more than two million Palestinians. An expansion of the conflict to include Hamas’s Iranian-backed ally, Hezbollah, in Lebanon would be a development that some feared would multiply the regional despair.

In Israel, activity in many sectors of the economy has slowed or ground to halt. The tourism business has come to a near standstill, with cruise ships avoiding Israel’s shores and people canceling visits. Major airlines have halted flights to and from the country, including for cargo. On Monday, UPS said it had stopped flying to Israel. Sea freight operations have faced additional controls by the Israeli Navy, affecting cargo shipments. Israel, which relies heavily on imported oil, has shut one of its two main oil ports for safety reasons, analysts said.

Tech companies and start-ups reported that many of their younger employees had been mobilized. Nvidia, the world’s largest maker of chips used for artificial intelligence and computer graphics, said it had canceled an A.I. summit that was scheduled to take place in Tel Aviv. Retailers, including H&M and Zara, have shut stores in the country.

The Israel-Gaza conflict could also slow natural gas investment in the area, analysts said, hurting the ambitions of Israel and the wider region, which have recently received a lift from Chevron to become a hub for exporting natural gas to Europe and elsewhere.

Mr. Yaron, the central bank governor, said on Sunday that the Israeli economy had “known how to function and to recover from difficult periods in the past, and to return to prosperity rapidly.”

Even so, Mr. Yaron said, with many reserve soldiers at the front lines and civilians in shelters because of rocket attacks, there will be an effect on real economic activity. And war, he added, was “likely to persist in the coming period.”

“History has taught us that when terrorists don’t pay a price for their terror, when dictators don’t pay a price for their aggression, they cause more chaos and death and more destruction,” Mr. Biden said from behind the Resolute Desk. “They keep going. And the cost and the threats to America and the world keep rising.”

The president delivered the speech as his administration braces for opposition to his request for $74 billion in assistance for the two countries. The money would pay for weapons and other military equipment as Israel responds to the Oct. 7 attacks by Hamas and Ukraine fights on in its 600-day war to expel Russian invaders.

The president’s efforts to build support for a major projection of American influence abroad come against the backdrop of a deeply fractured population at home, political dysfunction in Congress, economic uncertainty and the possibility of an election-year rematch against a former president facing multiple criminal indictments.

In the days ahead, Mr. Biden is sure to face questions about whether the United States can afford to be financing two foreign wars. Although the U.S. economy has proved remarkably resilient this year, new data is expected to show on Friday that the deficit approached $2 trillion this fiscal year, and inflation remains uncomfortably high.

On Thursday, Mr. Biden described his request for aid as “a smart investment that’s going to pay dividends for American security for generations.” But he faces skepticism among members of both parties: progressive Democrats who fiercely oppose sending arms to Israel and conservative Republicans who have questioned the need to add to the more than $100 billion already approved in military and economic aid already sent to Ukraine.

And the president’s request arrives on Capitol Hill at a time of turmoil among House Republicans, who have failed for 16 days to pick a speaker. The political paralysis has left lawmakers unable to act on legislation, including new aid for either Ukraine or Israel.

In his speech, Mr. Biden urged lawmakers to resolve their differences and come together swiftly to embrace America’s role as what he called the “essential” country.

“American leadership is what holds the world together,” he said. “American alliances are what keep us, America, safe. American values are what make us a partner that other nations want to work with.”

“To put all that at risk,” he added, “if we walk away from Ukraine, if we turn our backs on Israel, it’s just not worth it.”

He said other groups were also holding some of the hostages, though he specified only Palestinian Islamic Jihad, a separate organization that is an ally of Hamas, the group that controls Gaza and that staged the attack on Israel earlier this month.

The Israeli military has said that 203 people, including civilians and soldiers, are being held by Hamas. The hostages were taken on Oct. 7, when hundreds of Palestinian gunmen from Gaza surged into towns and military bases in Israel. More than 1,400 Israelis were killed.

A spokesman for Palestinian Islamic Jihad, Musab Al-Breim, said in an interview that the group had around “30 prisoners” but would not share the exact number.

That other groups besides Hamas are holding hostages could complicate efforts to secure their release, officials with knowledge of the hostage talks said.

One diplomat with knowledge of the situation, who spoke on the condition of anonymity to discuss sensitive negotiations, said Hamas did not expect to take so many civilians captive.

The diplomat said that the Palestinian gunmen who carried out the attacks, which included some from the more ideologically extreme group Islamic Jihad, were surprised at how deep they were able to advance and the ease with which they were able to take civilians and soldiers hostage.

“The success of the attack was significant,” Mr. Hamdan said. “No one expected that, and it showed the fragility of the Israeli military.”

Mr. Hamdan said Hamas was seeking a broad prisoner exchange and was requesting that Israel free women, children and hundreds of Palestinians who have been held without trial. Israel is currently detaining at least 1,100 Palestinians without trial, the most since 2003, according to HaMoked, an Israel-based human rights organization.

“Everyone knows that we have tried to free the Palestinian prisoners,” Mr. Hamdan said. He added, “This isn’t a Hamas issue, but a Palestinian one.”

A second diplomat with knowledge of the hostage talks said Hamas had requested a cease-fire to hand over the civilians it holds.

The hostages from countries other than Israel may be treated differently. Hamas’s military wing has said that “civilian prisoners with foreign nationalities are guests and will be released when field conditions allow so,” Ezzat Al-Resheq, a member of Hamas’s political bureau in Beirut, said in an interview.

“They are not part of any deal, and we have no demands in return for releasing them,” he added.

Hamas, however, intends to hold Israeli soldiers as part of a larger prisoner exchange, said the first diplomat with knowledge of the hostage situation.

A 2020 report by Save the Children estimated that up to 700 Palestinian children are detained and prosecuted by the Israeli military court system each year. Most are charged with stone throwing, which carries a maximum sentence of 20 years’ imprisonment.

Mr. Hamdan said Israel’s occupation of what his group considers Palestinian territory was “the main problem from which the other problems flow.”

“The Israelis have to decide,” he said. “Do they want to continue with the occupation? Or do they want to make a change by acknowledging Palestinian rights and endorsing international resolutions?”

Yousur Al-Hlou contributed reporting from Cairo, and Abu Bakr Bashir from London.

Last month, the Homeland Security and State Departments announced that Israel would be added to its visa-waiver program, an agreement between the United States and 40 other countries that allows citizens to travel without the hassle of getting a visa. At the time, the Biden administration set a Nov. 30 date for when Israelis could begin applying online for the new program.

To participate, countries must share information about passengers faster, including providing names on passenger lists.

To be eligible, Israeli citizens must have a biometric passport. And they must commit to staying no longer than 90 days. The application comes with a $21 fee.

Allowing Israel into the program has been a decade-long process. Some prominent groups have objected to Israel’s being allowed into the program out of concerns that the Israeli government would not treat Palestinian Americans equally.

Tensions intensified on Tuesday after a deadly blast at a hospital in Gaza left Hamas and Israel trading blame. In Turkey, pro-Palestine supporters tried to enter a U.S. military base in the city of Malatya and demonstrated outside the U.S. consulate in Istanbul. On Thursday, a spokesman for Hamas called for further protests outside of American and Israeli embassies.

Here’s what you need to know if you’re considering international travel.

What does the advisory mean?

The advisory calls on Americans to be vigilant while traveling and to stay alert at tourist sites. It also urges U.S. citizens to enroll in the government’s Smart Traveler Enrollment Program to receive information and alerts and to make it easier to be located during an emergency overseas.

The worldwide caution notice was last issued in 2022 after the killing of Ayman al-Zawahri, which led the State Department to warn travelers that Al Qaeda might try to attack Americans traveling abroad.

Should I change or cancel my travel plans?

Probably not — but it depends on where you’re going.

Before traveling, visitors should check the State Department’s website for country-specific guidance. The travel advisory for Israel and Lebanon was raised to the highest level this week, warning citizens not to travel to Lebanon and Gaza and to reconsider travel to Israel and the West Bank. Some U.S. government personnel were authorized to depart from those regions.

Tens of thousands of pro-Palestinian supporters have marched across cities like London, Paris and Rome this week to protest the Israeli bombardment of Gaza. Local authorities have ramped up security.

For most European countries, a Level 2 advisory is in place, urging U.S. citizens to “exercise increased caution” because of terrorism threats and civil unrest. Paris and Brussels are on high terrorism alerts after recent attacks and threats led to the evacuation of several airports and tourist sites like the Louvre Museum and the Palace of Versailles.

Have international flights been affected?

Major U.S. airlines suspended service to Israel after the initial attack by Hamas on Oct. 7, but Ben-Gurion International Airport in Tel Aviv remains open, and commercial flights are still available.

The U.S. government has been arranging charter flights for U.S. citizens who want to leave Israel.

The missiles and drones were launched by pro-Iranian Houthi rebels in Yemen amid a flurry of drone attacks against American troops in Iraq and Syria over the past three days, General Ryder said. The incidents underscored the risks that the conflict between Israel and the Palestinian group Hamas could spiral into a wider war.

Military analysts were trying to determine who carried out the drone attacks, General Ryder said, but Iran-backed militias have in the past conducted drone and rocket attacks against the 2,500 American troops based in Iraq and the 900 troops in Syria.

Since Hamas’s terrorist attacks against Israel on Oct. 7, the Biden administration has rushed two aircraft carriers and additional troops to the eastern Mediterranean near Israel to deter Iran and its proxies in the region from engaging in a regional war.

Israel has responded to the Hamas attacks with airstrikes and a “complete siege” of Gaza, which the group controls.

Senior Biden administration officials and American commanders have expressed fears that the United States could get dragged into the conflict if the militias attacked U.S. forces in Iraq and Syria.

General Ryder sought to stay on that theme on Thursday despite what he acknowledged was “an uptick” in drone attacks in Iraq and Syria in the past few days.

“Right now, this conflict is contained between Israel and Hamas, and we’re going to do everything we can to ensure deterrence in the region, so that this does not become a broader” conflict, General Ryder said.

Iranian officials, however, have publicly warned that new fronts against Israel could open in the region if its offensive on Gaza continued.

A deputy commander of Iran’s Islamic Revolutionary Guards Corps, Gholamhossein Gheybparvar, said in a speech on Thursday that Iran-backed militia in Syria, Iraq, Yemen and Lebanon — known as an “axis of resistance” — were ready to strike Israel if its ground forces invaded Gaza.

On Wednesday, Iran’s state television aired a segment detailing how such attacks could unfold.

The report opened with the country’s supreme leader, Ayatollah Ali Khamenei, saying that if the war continued “nobody could stop the forces of the resistance,” referring to a network of militia groups across the region supported by Iran.

Houthis in Yemen from the south, Syrian and Iraqi militias from the east, and Hezbollah in Lebanon from the north would coordinate to attack Israel with missiles and drones to create “a siege from every side,” the report claimed. The segment said that the Houthis had missiles with a range of more than 1,200 miles.

The report said Iraqi militia groups had taken positions alongside Syrian militias near the Golan Heights, an area Israel captured from Syria in 1967 and later annexed.

Iran’s state television routinely broadcasts propaganda and hyperbole, and the military threats could be part of a strategy to fuel growing anxiety in the region.

At the Pentagon on Thursday, General Ryder said that any armed American response to this week’s attacks, “should one occur, will come at a time and a manner of our choosing.”

In March, U.S. intelligence agencies concluded that a self-destructing drone of “Iranian origin” killed a U.S. contractor and injured another contractor and five U.S. service members in an attack on a maintenance facility on a coalition base in northeast Syria.

President Biden retaliated by ordering the Pentagon to carry out airstrikes against facilities in eastern Syria used by groups affiliated with Iran’s Revolutionary Guards.

The latest spate of attacks continued on Wednesday morning when U.S. and coalition forces at the Al Tanf base in southern Syria fired on two drones, destroying one, while the other slammed into the base, causing “minor injuries,” General Ryder said.

About 200 American troops are stationed at Al Tanf, whose main role is training Syrian militias to fight the Islamic State.

At the same time on Wednesday, alert sirens wailed at Al Asad Air Base, a sprawling installation in western Iraq. Though no drone or rocket attacks happened, a civilian contractor, whom the military did not identify, suffered a heart attack while sheltering and died soon afterward, General Ryder said.

On Wednesday, the military’s Central Command said that it had intercepted several drones in Iraq in the previous 24 hours that were menacing American military and other allied personnel in the country.

American forces attacked two drones at Al Asad, destroying one and damaging the other, resulting in “minor injuries” to coalition troops, the command said in a statement. Separately, in northern Iraq, the military destroyed one drone, resulting in no injuries, the command said.

There were unconfirmed reports on social media of additional drone attacks in Syria late Thursday.

“Clearly, this is an uptick in terms of the types of drone activity we’ve seen in Iraq and Syria,” General Ryder said.

Pentagon officials warned that the cruise-missile and drone attacks could augur an escalation of violence that could endanger American forces in the region and potentially draw them into a conflict.

In November 2021, American and Israeli officials said that an armed drone strike a month earlier against Al Tanf was Iranian retaliation for Israeli airstrikes in Syria.

The attack caused no casualties, but it represented the first time Iran had directed a military strike against the United States in response to an attack by Israel.

But on Oct. 7, when Hamas attacked his kibbutz, Mr. Bowom encountered hundreds of Hamas fighters at the kibbutz gate after being picked up from his home and driven there, Mr. Revivo said a military official told the family.

“They fought with them and managed to kill a few, but then ran out of ammunition,” he said. “Gil was shot a couple times, fell and lost consciousness. Another member of the alert team picked him up and brought him to a dentist’s office, where first aid workers were stationed.”

He died a half an hour later, a nurse told his wife, Ayelet Bowom. He had been shot twice in the legs and the first aid workers could not find any exit wounds.

It’s been nearly two weeks since Gil Bowom and the couple’s son, Inbar, walked out of their homes to defend their city, Kibbutz Be’eri, from Hamas’s attack, never to be seen alive again.

Ms. Bowom and her three surviving children finally received their bodies and held their funerals on Tuesday. Now she and her brother are piecing together scraps of information to figure out what happened to them, and she and her son, Adi, are trying to recover from their own traumatic experience of hiding from Hamas while they ransacked her house.

The family’s experience underscores that as Israel prepares to launch a ground invasion in Gaza, many survivors are still mourning their losses.

“All my body is shouting ‘why them’ because they were like angels,” Ms. Bowom said. “Both of them have good faith and pure hearts,” she added.

On Oct. 7, shortly after Be’eri came under attack in the early morning, Mr. Bowom’s husband, a print shop worker who volunteers as a member of an alert team, got called to duty and her 22-year-old son, Inbar, a security worker who had just finished an overnight shift, got called back to work.

Ms. Bowom stayed behind with her 16-year-old son and hid with him in a 96-square-foot bunker for 10 hours. During that time, Hamas terrorists broke into her home, staying for several hours while she and her son kept quiet, fearing they would be killed.

Ms. Bowom, a 54-year-old mother of four, and her brother, Mr. Revivo, spoke to The Times from their sister’s home in Gane Tikva, where they are staying with Ms. Bowom’s three other children and about a dozen other family members.

Ms. Bowom said she was told by a nurse who tried to help her husband that Inbar’s death came even quicker. Ms. Bowom and Mr. Revivo said that he had just arrived at his girlfriend’s apartment after the overnight shift when he was called back.

“We lost contact with him as he was driving back,” Mr. Revivo said, adding that days later he was identified through DNA. They think he was ambushed, he said.

“He could have said no, but he’s not that type of person,” Ms. Bowom said of her son. “He always wanted to keep his friends and his family safe,” she added.

Still in mourning, she said that she doesn’t know what life in Israel will be like going forward or where she can feel safe. “We have no other place to go,” she said. “It’s not like it’s safer for Jews elsewhere.”