Though Mr. Blinken did not provide details, a senior U.S. official said he was referring to the possibility that Israel might be willing to pause its Gaza offensive briefly in return for a small number of hostages. According to Israeli officials, Israel has recently discussed with Egypt the possibility of a shorter cease-fire — lasting roughly a week and a half — in exchange for the release of some of the 101 hostages in Gaza, many of whom are presumed dead.

That would be a departure from the plan that’s been on the table for months, which laid out a path to free all the hostages in exchange for the release of thousands of Palestinian prisoners and an Israeli commitment to end the war.

U.S. officials are hoping to test whether Hamas is more open to negotiations following the death last week of its leader, Yahya Sinwar, whom Mr. Blinken on Wednesday called “the primary obstacle” to a larger agreement. U.S. officials would also welcome even a short pause in the fighting to allow humanitarian aid to surge into Gaza, which could create space for further negotiations.

The senior official noted that the U.S. was open to the new, limited approach but said the Biden administration was not actively promoting it. Mr. Blinken also reiterated in his meeting with the hostage families his public commitment to freeing all the hostages, leaving none behind, the official said.

It is unclear whether such an approach is any more likely to succeed than past ones. Hamas has said it will not release any more hostages without an Israeli commitment to end the war, and its surviving leaders have signaled no softening of their position since the death of Mr. Sinwar.

Aaron Boxerman contributed reporting.

The Israeli military has repeatedly asserted over the past few days that Hezbollah — the powerful Lebanese armed group backed by Iran — had stashed hundreds of millions of dollars in an underground command center beneath al-Sahel hospital.

Fadi Alameh, the hospital’s director, called the claims baseless and invited international observers to visit the hospital. Journalists who arrived on a supervised tour on Tuesday reported no evidence of any underground bunker or hoards of wealth.

On Wednesday, Nadav Shoshani, an Israeli military spokesman, accused Hezbollah of masking the entrance to the site and preventing reporters from accessing it. “Hezbollah doesn’t want you to find the money,” he added.

It is a war of words with a now-familiar ring to it: Israel has repeatedly surrounded and raided hospitals in the Gaza Strip in its yearlong war there, accusing Hamas of using them for military purposes. Hamas has denied the claim, although at least some returned Israeli hostages have testified that they were held captive inside Gaza hospitals.

Mr. Austin said Hezbollah had a history of placing weapons beneath mosques and schools and using civilian sites as cover for military operations. Both groups have denied the claims.

“The Israelis need to be as careful as possible to protect civilians,” Mr. Austin said, but added that Hezbollah and Hamas’s tactics were making that “more complicated.”

Euan Ward contributed reporting.

The current round is administering a second dose of the vaccine, which the agencies said should be given within six weeks of the first dose to maximize its impact. The first round of doses in northern Gaza was completed on Sept. 12.

“Having a significant number of children miss out on their second vaccine dose will seriously jeopardize efforts to stop the transmission of poliovirus in Gaza,” the statement said. “This could also lead to further spread of poliovirus in the Gaza Strip and neighboring countries, with the risk of more children being paralyzed.”

Aid agencies including the World Health Organization were aiming to administer doses to about 120,000 children in northern Gaza. A spokesman for UNICEF, Joe English, said there was only a “matter of days left to ensure the second dose of the vaccine is delivered to children within the scheduled window.”

The anti-polio campaign has depended on an agreement by Israel and Hamas to observe temporary pauses in fighting in areas where the vaccinations are taking place, and a largely successful first round of doses in September was a rare bright spot in the war, according to aid agencies. But the area of northern Gaza where the pause was in effect had been “substantially reduced” and was now limited only to Gaza City, and as a result, many children would have missed out on the vaccinations, the statement said.

Last week an airstrike hit a compound that was to have been used for vaccinations in the town of Nuseirat, killing several people, according to UNRWA, the main U.N. agency that aids Palestinians in Gaza.

Some Palestinians in Gaza have said the vaccination drive was futile given the dangers posed by the war and Israeli airstrikes. Israel has begun a renewed military offensive in northern Gaza in recent weeks that it says aims to prevent Hamas, which led the deadly attacks on Israel last October, from attempting to make a comeback.

The Israeli military has told civilians to flee a large part of northern Gaza and has carried out deadly airstrikes there. Palestinians have said that the Israeli operation in Jabaliya, a town north of Gaza City, has been one of the heaviest of the war.

The Israeli government agency that oversees its policy in Gaza and the occupied West Bank, COGAT, said on social media on Wednesday that vaccinations in northern Gaza would begin “in the coming days” after an assessment with U.N. agencies. The Israeli military did not have an immediate comment and said it was checking reports of the postponement.

COGAT said the second round of the campaign was completed in southern Gaza a day earlier. It said the vaccination campaign in northern Gaza would begin in the coming days after an assessment with U.N. agencies.

“We’ve been busy,” said Mortada Mhanna, the head of Tyre’s disaster management unit, who coordinated efforts on Wednesday to move civilians to safety.

Israel has previously targeted Tyre with airstrikes in the weeks since its forces invaded southern Lebanon, but this was the first time it had called for evacuations in such a large portion of the city. The warning posted on social media on Wednesday covered an area equivalent to several city blocks.

Tyre is one of the oldest continuously inhabited cities in the world and is home to Roman ruins that attract international tourists. The city had around 125,000 residents before the war, but many have fled in recent weeks amid Israel’s offensive against Hezbollah, the powerful Lebanese militant group.

The Israeli military said that it had targeted command centers in Tyre belonging to Hezbollah, and accused the group of embedding in civilian areas.

Around 15,000 people still lived in Tyre when the Israeli military issued the evacuation warning, Mr. Mhanna said. Many had fled to Tyre’s Christian quarter or took refuge along the coast, believing they would be safer there, he said.

Local emergency services workers had spent the morning driving through the city’s streets with loudspeakers in an attempt to warn civilians of impending bombardment. Hours later, the Israeli military began to target the area, sending huge clouds of smoke towering above the city.

The U.N. refugee agency said last week that more than a quarter of Lebanese territory was now under Israeli evacuation warnings. At least one million people in Lebanon — around a fifth of the population — have been displaced, dispersed among schools, sleeping on sidewalks and taking shelter in abandoned buildings.

Lebanon’s culture ministry condemned the attacks in Tyre in a statement and called on UNESCO to intervene to protect the archaeological sites.

“The smell of death is everywhere as bodies are left lying on the roads or under the rubble,” Mr. Lazzarini said of northern Gaza. “Missions to clear the bodies or provide humanitarian assistance are denied. In northern Gaza, people are just waiting to die.”

Gloria Lazic, an aid worker with the U.N. agency for humanitarian coordination, OCHA, said Tuesday on social media that requests by the agency to help people trapped under the rubble in the Faluja area of Jabaliya, in northern Gaza, had been “repeatedly denied by Israeli authorities” over five days, imperiling the lives of potential survivors.

“We’re talking about more than 40 people, three families, who have seen their houses collapse above them,” Ms. Lazic said. “And we don’t know if we finally get this approval, how many will still be alive.”

On Tuesday, the Gazan Health Ministry, which does not distinguish between civilian and combatant deaths, said that Israeli attacks over the last two days had killed 115 people and injured more than 480 others. Some victims, the ministry said, were still under the rubble.

COGAT, the Israeli agency that oversees policy for the Palestinian territories, did not immediately respond to a query about Ms. Lazic’s post about being denied permission to search for survivors.

But COGAT recognized the international community’s alarm about the dire situation in Gaza. Last week, in an emergency U.N. Security Council meeting, Council members displayed rare unity, unanimously calling on Israel to immediately address a falloff of aid and supplies reaching the enclave.

The United States on Oct. 13 also warned Israel in a letter that it risked losing military assistance if it failed both to increase aid flow into Gaza and to comply with its humanitarian obligations.

On Tuesday, COGAT and the Israeli military said in a joint statement that since Oct. 14 — the day after the United States issued the warning letter — more than 230 trucks with food, water, medical supplies and shelter equipment from Jordan and the international community had been transferred to northern Gaza. The Israeli authorities “will continue to act in accordance with international law to facilitate and ease the humanitarian response to the Gaza Strip,” the statement said.

In a separate update on humanitarian assistance in Gaza issued by COGAT on Tuesday, it said that 478 aid trucks had entered the enclave from Oct. 14 to Oct. 20.

The latest numbers still fall far short of the minimum amount of assistance that experts say is required to meet the needs of the 2.2 million people in the besieged enclave. At least 350 aid trucks per day must be allowed to enter Gaza, the U.S. warning letter to Israel said.

COGAT has argued that U.N. agencies are not moving the aid that reaches the enclave. In a post on social media on Monday, COGAT said there were “600 trucks worth of aid waiting to be picked up and distributed, the majority by @UN aid agencies.”

Disputes between COGAT and U.N. agencies over aid in Gaza have persisted throughout the war. But hunger in northern Gaza has worsened, and the World Food Program this month said there was a risk of famine for the roughly 400,000 people living under bombardment there.

Mr. Safieddine, a cousin of Mr. Nasrallah and one of Hezbollah’s top officials, was presumed to be at that meeting.

On Tuesday, the Israeli military said Mr. Safieddine was killed in a strike about three weeks earlier. Mr. Safieddine had a significant influence over Hezbollah and served as the group’s leader when Mr. Nasrallah was not in Lebanon, according to a statement from the Israeli military.

“Throughout the years, Safieddine directed terrorist attacks against the state of Israel and took part in Hezbollah’s central decision-making processes,” the statement said, adding that more than 25 Hezbollah operatives were present at the meeting where the military struck and killed Mr. Safieddine.

The Israeli military on Tuesday did not provide any proof for its assertion that Mr. Safieddine was dead and Hezbollah had generally avoided commenting on his fate in the weeks after the strike. On Wednesday, Hezbollah confirmed that Mr. Safieddine was dead.

“We have reached Nasrallah, his replacement and most of Hezbollah’s senior leadership,” Lt. Gen. Herzi Halevi, chief of the general staff of the Israeli military, said in a statement. “We will reach anyone who threatens the security of the civilians of the state of Israel.”

Mr. Safieddine’s death would come as yet another crushing blow for Hezbollah, which many in Lebanon now consider rudderless amid the Israeli assassination campaign against its leaders.

On Oct. 7, Prime Minister Benjamin Netanyahu suggested that Israel had killed Mr. Safieddine, but stopped short of naming him.

“We took out thousands of terrorists, including Nasrallah himself and Nasrallah’s replacement,” Mr. Netanyahu had said, an apparent reference to Mr. Safieddine.

The loss is another blow to Hezbollah’s leadership ranks, which have been decimated in Israel’s expanding campaign against the Iranian-backed group.

Mr. Safieddine, born in southern Lebanon in the early 1960s, was one of Hezbollah’s earliest members. He joined after the Shiite group was formed, with Iranian guidance, in the 1980s during Lebanon’s civil war. He rose quickly in the group alongside Mr. Nasrallah, playing many roles and serving as a political, spiritual and cultural leader. He also led Hezbollah’s military activities at one point.

Like Mr. Nasrallah, Mr. Safieddine usually appeared in a black turban, marking him as a revered Shiite cleric who could trace his ancestry back to the Prophet Muhammad. And like his cousin, Mr. Safieddine studied in Iran: He pursued religious studies in the city of Qom before returning to Lebanon to work for Hezbollah.

He was close friends with Maj. Gen. Qassim Suleimani, who commanded the Islamic Revolutionary Guards Corps’ Quds Force in Iran until the United States killed him in an airstrike in Baghdad in 2020. Later that year, Mr. Safieddine’s son married the Iranian general’s daughter in a much-publicized wedding that some analysts and critics point to as emblematic of Iran’s entrenchment in Hezbollah.

The United States and Saudi Arabia designated Mr. Safieddine a terrorist in May 2017 for his Hezbollah leadership role. At the time, the State Department described him as “a senior leader” in Hezbollah’s Executive Council, which oversees the group’s “political, organizational, social and educational activities.”

The United States had designated Hezbollah a terrorist organization two decades earlier, and holds the group responsible for several attacks that killed hundreds of Americans, including the bombings of the American Embassy and U.S. Marine barracks in Beirut in the early 1980s, and the 1985 hijacking of TWA Flight 847.

Farnaz Fassihi, Euan Ward and Aaron Boxerman contributed reporting.

Photographs published in the Israeli news media on Tuesday showed damage to an upstairs window of the Netanyahus’ Caesarea home, as well as damage to the grounds.

The couple are known to have often spent weekends at their home in Caesarea, a well-to-do coastal town. Their locations are more often kept secret nowadays, for security reasons.

Mr. Netanyahu has called the episode a “grave mistake,” and his allies have warned that it will not go unanswered.

After the prime minister met on Tuesday with Secretary of State Antony J. Blinken in Jerusalem, Mr. Netanyahu’s office said Mr. Blinken had “expressed the U.S.’s deep shock over the Iranian attempt, via Hezbollah, to eliminate the Prime Minister of Israel, and made it clear that this was an exceptionally extreme incident.” Mr. Netanyahu thanked Mr. Blinken and said that this was “a dramatically significant issue that must not be ignored,” the statement added.

Also on Tuesday, in what appeared to be an implicit effort to distance Iran from responsibility for the attack, Hezbollah, at war with Israel, said it was fully responsible for the drone strike. Mohammad Afif, Hezbollah’s media chief, made the claim at a news conference.

Hezbollah’s statement comes as Israel is preparing for an attack on Iran in retaliation for Iran’s recent launching of nearly 200 ballistic missiles at Israel. That assault, in turn, came in response to the assassinations of Hezbollah’s leader, Hassan Nasrallah, in September; Hamas’s political leader, Ismail Haniyeh, during a visit to Tehran in July; and an Iranian commander.

The Israeli military’s chief spokesman, Rear Adm. Daniel Hagari, said in a televised statement on Saturday night that “the fighting will only increase” after that morning’s drone strike, which he characterized as an “attempt to harm the prime minister.”

The military had said only that the drone struck “a building” in Caesarea, without elaborating.

The strike on the house underlines the challenge unmanned vehicles pose to Israel’s air defense. Drones can carry out precise strikes, and are difficult to detect and intercept, in part because they fly at low altitudes.

The strike in Caesarea came nearly a week after a Hezbollah drone attack killed four soldiers and wounded dozens of others as they sat in the dining hall of a military base in northern Israel.

The statement came a day after the police said they had dismantled a separate spy network made up of seven Jewish Israelis whom the authorities accused of gathering intelligence for Iran. It was not clear when those suspects were arrested or why both spy cases were made public this week.

The suspects arrested from East Jerusalem had been taken into custody in recent weeks and have yet to be indicted, according to the statement on Tuesday, which described them as residents of Israel. They were from the Beit Safafa neighborhood, which is populated mainly by Palestinians.

Some of the suspects took photographs of the scientist’s house in preparation for the assassination attempt, according to the statement, which said they also had planned to blow up a police vehicle and throw a grenade at a house in return for the equivalent of around $50,000 in total.

The statement gave few details of the identities of the suspects but it said that one, a 23-year-old Israeli citizen, had recruited the others. They were then directed to spray graffiti in a different part of Jerusalem, set fire to cars and gather intelligence, the statement said. The statement gave no reason for why those targets were suggested.

Israel’s government has said it will retaliate against Iran for a drone and missile attack carried out against Israel on Oct. 1. Direct conflict between Israel and Iran broke out in April after a clandestine war that had lasted for decades.

The English language version of Iran’s state news agency, IRNA, has made no mention of the two cases or carried any response from the Iranian authorities to the allegations.

The neighborhood where the suspects lived is mostly part of East Jerusalem, which was captured by Israel from Jordan in 1967 and later annexed. Israel considers all of Jerusalem its undivided capital, but most East Jerusalem residents are Palestinians who want East Jerusalem to be the capital of a future Palestinian state. The United Nations Security Council has deemed it occupied territory.

The police said on Tuesday that, following a separate investigation with other Israeli security agencies, they have recently indicted a man who was planning to attack a demonstration on behalf of hostages held in Gaza. It gave no further details of that plot.

“We’re hearing his phone ringing. It keeps ringing under the rubble,” said Mpsati Mi, 30, an Ethiopian national who was searching for her friend, Aamal.

“He’s not only a neighbor, but a brother to me,” she said.

“I tried to call,” said another local resident, Ahmad Kalash, a Syrian national who had already visited nearby hospitals to see if he could find his friend, Hussein.

“I’m waiting to hear anything from the rescuers,” he said.

At least 18 people, including four children, were killed in the strike, and 60 others were wounded, according to Lebanon’s health ministry. The attack, which was not preceded by an evacuation notice from the Israeli military, also damaged the nearby hospital, which in recent weeks has been swamped by patients evacuated from other health facilities.

The Israeli military said that it had not targeted the hospital, and had instead aimed at a “Hezbollah terror target” in the area. The military said that the hospital had not been affected, but damage was seen during a visit to the facility by a Times reporter and photographer on Tuesday.

The powerful blast had shattered the hospital’s windows and the solar panels affixed atop the building, a lifeline amid Lebanon’s chronic power shortages. Rows of sand bags now lined the underground parking lot as hospital workers made preparations for further strikes. Many of them were in an uproar, saying they did not have the staff numbers and supplies they needed.

“The hospital was subjected to severe damage,” said Dr. Jihad Saadeh, the hospital’s director, recounting how two missiles had flattened at least three buildings opposite the main gate.

Israel began an intensified military campaign against Hezbollah last month, nearly a year after the Lebanese militant group began firing rockets into Israel in solidarity with Hamas in Gaza. The Israeli offensive has set off a humanitarian crisis in Lebanon, displacing around a fifth of the population and buckling the country’s health sector.

The conflict has killed more than 2,400 Lebanese over the past year, most of them in recent weeks, according to Lebanon’s health ministry. Hundreds of women and children are among the dead.

At the scene of the strike, one man said he had lost eleven of his relatives — among them women and children. Other local residents described panic and terror when the overnight strike hit, and said that people who had been displaced from other parts of the country by Israel’s offensive were among the dead.

“The shock wave pushed us. I felt I was flying,” said Ahmad al-Hassan, 48, who was at home with his wife and children when the blast struck. His home survived the explosion but was badly damaged. He was one of the lucky ones.

Hassan Hakim stood waiting at the site for news about his friend, Mohamed, who was still trapped under the rubble along with his two children.

“I saw a hand,” said Mr. Hakim. “I don’t know whether it’s Mohamed or not.”