“We’re not leaving,” said Mr. Sidu, 31, in a phone interview on Thursday.

The fliers, dropped over parts of the city by Israeli warplanes and posted on social media, did not directly call on people to leave their homes and shelters, but laid out four “safe corridors” for them to flee south to central Gaza “quickly and without inspection.”

“Gaza City will remain a dangerous combat zone,” the fliers warned.

But few appeared to be heeding the warning. In interviews, people in the city said they had decided to stay in their homes or in places where they have been sheltering — including relatives’ homes, hospitals and schools — fearing the potential dangers from Israeli forces on the evacuation routes, and knowing there is no safety in the south.

The United Nations has said repeatedly that the Israeli offensive in Gaza has left nowhere safe. Palestinians there have been forced to flee multiple times amid shifting orders and flare-ups in fighting.

“People have been steadfast now for nearly 270 days, and they won’t be displaced,” even if Israel occupies all of Gaza, Mr. Sidu said. “In my family we agreed that no one will be displaced, and this is how families are in Gaza, despite the lack of water, food and all life’s necessities.”

“The fact is people are being killed wherever we are, either in the north or in the south,” he added.

One Gaza City neighborhood, Shajaiye, was left in ruins after an Israeli ground offensive there ended on Wednesday. The Palestinian Civil Defense said that rescue crews had so far recovered approximately 60 bodies from the rubble, and that more than 85 percent of buildings in the neighborhood had been destroyed, leaving the area uninhabitable.

Rescuers were struggling to reach victims in other areas of Gaza City where Israeli ground troops are still active, including the Tal al Hawa neighborhood, the Civil Defense said.

The United Nations estimates that there are now some 300,000 people in northern Gaza, which includes Gaza City. Since last month, Israeli forces have launched offensives on several parts of the city, saying they were returning to fight remnants of Hamas and other armed Palestinian groups. Israeli forces have been going back to parts of Gaza that they had previously left, especially in the north, which they invaded in October, as Hamas regroups. Their return has sparked new exoduses from those areas.

“People are on the run everywhere,” said Juliette Touma, a spokeswoman for UNRWA, the United Nations agency that helps Palestinians. “It’s probably one of the toughest decisions in life that one can make to leave everything behind.”

Israel first ordered hundreds of thousands of Gazans in the northern part of the territory to flee south in mid-October, a week after the Hamas-led attack on Israel.

Naheel Mehanna, a 41-year-old writer from Gaza City, saw the new leaflets on social media but not in her neighborhood. The Israeli military also calls people multiple times a day with a recorded message warning them to flee south, she said.

“I know this is a message of fear; they want to terrify us to leave,” Ms. Mehanna said. “This is why they continue to call people over the phone, because no one is listening to them, no one is leaving.”

Ms. Mehanna said her friends who fled to the south earlier in the war continue to warn her against leaving Gaza City. “They say it is not safe there at all,” she said.

Gazans also don’t trust assurances by the Israeli military that the evacuation routes are safe. Israeli forces have detained thousands of Gazans, including men of all ages, women and children. Many were stopped as they fled their neighborhoods with their families after the military ordered them to leave.

“There is no opportunity for people to flee south,” said Amani Zanin, 30, who is staying with her parents and numerous aunts and uncles in Gaza City. “The road is not safe.”

The extended family has already been displaced multiple times in northern Gaza and is now sheltering in a school building.

The trip south has to be made on foot, as the Israeli military doesn’t allow vehicles on part of the route. That could take up to four hours, and all that walking in the summer heat would be too much for some of her older relatives.

“It is difficult for us to go south,” Ms. Zanin said. “We heard about leaving, but we haven’t seen anyone who has left.”

Abu Bakr Bashir and Ameera Harouda contributed reporting.

The Israeli military’s investigation into the devastating attack on Be’eri, where over 100 Israeli civilians were killed, marks the beginning of a national reckoning. It is the first of dozens of inquiries set to examine how and why Israel failed to protect its citizens from Hamas’s devastating assault, though critics and some survivors have raised questions about the military’s ability to transparently investigate its own failures.

“This is the beginning of a long process of repair and rebuilding trust between the Israel Defense Forces and the public,” Rear Adm. Daniel Hagari, the Israeli military spokesman, told reporters on Thursday night.

In a statement summarizing the results of the investigation, the Israeli military conceded that it had “failed in its mission” to protect Be’eri and detailed a series of errors, including disorganization, a lack of coordination between forces and slow response times. The Hamas-led attack began at dawn on Oct. 7 and continued through the next day.

“In the first seven hours of fighting, the residents of Kibbutz Be’eri fought almost alone against the enemy,” Admiral Hagari said.

But the inquiry praised the actions of Brig. Gen. Barak Hiram, who led the fighting in Be’eri, the military said. The statement said General Hiram’s decision — together with other commanders — to fire the tank shells at the home was “professional and responsible.”. Rear Admiral Hagari said the shelling sought to pave the way for forces to break into the house and rescue the hostages.

The episode ignited a fierce debate inside Israel over whether the military had done enough to protect Israeli civilians as it sought to repel Hamas militants who had overrun towns and military bases near Gaza. All told, roughly 1,200 people, mostly civilians, were killed during the Hamas-led attacks, and another 250 were taken hostage, according to Israel.

In a statement, the Israeli military said that the investigators were “independent of the chain of command and not involved in the events themselves.” But one of those listed, Lt. Col. Elihay Bin Nun, served as General Hiram’s chief operations officer during the fight in Be’eri, raising questions about the inquiry’s independence.

Yoav Gallant, the Israeli defense minister, called on Thursday for an independent state commission that would investigate the Oct. 7 attacks. Prime Minister Benjamin Netanyahu of Israel has resisted calls to launch such an inquiry, saying questions of responsibility ought to be sorted at the end of the war.

“It must investigate everyone: the decision makers and implementers; the government, the army, and security forces,” said Mr. Gallant. “It must check me, the defense minister. It must check the prime minister.”

Despite some early warnings, Israeli officials dismissed the possibility that Hamas could pull off such a large-scale invasion. And at daybreak on Oct. 7, as thousands of Palestinian gunmen stormed the border under heavy rocket fire, the Israeli military — caught unprepared — mounted a sluggish, chaotic response, leaving thousands of Israelis trapped for hours in fortified safe rooms.

Be’eri’s surviving residents described a bitter sense of having been left to fend for themselves by the government and military for hours as Hamas militants killed and took the villagers hostage. Rami Gold, who joined a handful of others who sought to rebuff the Hamas invaders, said an independent state inquiry was necessary to reach the full truth.

“The government brought about this situation, and they must be held to account,” said Mr. Gold, a member of the village’s civilian response squad.

The inquiry listed a number of other problems with the military’s response. In the chaos, soldiers who did not understand the severity of the situation in the kibbutz gathered outside Be’eri without plunging into the fighting. Other troops prioritized evacuating wounded soldiers over civilians. The Israeli military said both decisions were key failures.

By late afternoon, Israeli soldiers were fighting their way into most of the border towns attacked by Hamas. General Hiram, a decorated commander who lost his eye in combat in Lebanon, took charge of the fray in Be’eri. His conduct prompted both praise and criticism of the decisions he took, particularly the move to authorize the tank fire on the house.

In an interview with The New York Times last year, General Hiram, recalled having ordered forces to “break in, even at the cost of civilian casualties” after heavily armed militants in the house fired a rocket-propelled grenade. He authorized the use of light tank shells, which he claimed could make a hole in the wall but “not necessarily kill everyone in the building.”

General Hiram said that he had greenlit the shelling after attempts to negotiate with the Hamas fighters inside reached a dead end. On Thursday, the Israeli military said commanders then ordered Israeli forces to ultimately break into the house after gunfire was heard, leading them to fear the hostages’ lives were in danger.

But some family members and residents were left wondering whether Israeli troops could have saved the hostages if they had taken a less heavy-handed approach.

On Thursday, the Israeli military briefed the Be’eri survivors on the inquiry at a hotel near the Dead Sea, where many of the kibbutz’s roughly 1,000 residents are still living in temporary housing over nine months after the attacks.

Omer Shifroni, three of whose relatives were killed in the hostage episode, said the military did not seem to have attempted a cover-up of its failures in Be’eri. But he said that the inquiry failed to reckon with how Israeli soldiers — including General Hiram — might have acted differently.

“The probe didn’t ask what the alternatives were,” Mr. Shifroni said. “I’m left with questions.”

On Wednesday, personnel from the military’s Central Command attempted and failed to reattach the makeshift pier to the beach in Gaza after rough seas forced operators to remove the structure several days ago to avoid damage, the Pentagon said.

In a statement, Maj. Gen. Patrick S. Ryder, the Pentagon press secretary, said the latest effort to re-anchor the pier failed because of “technical and weather-related issues,” recurring problems that The New York Times identified last month when it reported that military officials had warned aid organizations that the project could be dismantled as early as July.

General Ryder said in the statement on Thursday that the pier, support vessels and other equipment would return to port in Ashdod, Israel, “where they will remain until further notice. A re-anchoring date has not been set.”

Mr. Biden ordered the U.S. military to begin building the pier in March, at a time when he was being sharply criticized for not doing more to rein in Israel’s military response to the Hamas-led attacks of Oct. 7. At the time, health authorities were warning that Gaza was on the precipice of famine.

Mr. Sullivan explained that the pier was not as necessary as it once was because more land crossings to ship aid into Gaza had opened in recent weeks under pressure from the White House.

“The real issue right now is not about getting aid into Gaza,” he said. “It’s about getting aid around Gaza effectively. But there are a lot of things that we need to work through, including lawlessness and armed gangs. In some cases, Hamas itself is trying to disrupt and derail the delivery of humanitarian assistance.”

Still, humanitarian groups have complained that the pier has largely failed in its mission. In the nearly two months since it was first attached to the shoreline, the pier has been in service only about 20 days, military officials said. The rest of the time, it was being repaired after rough seas broke it apart, detached to avoid further damage or paused because of security concerns.

Asked if the temporary pier had been a success, Mr. Sullivan rebutted those criticisms.

“Look, I see any result that produces more food, more humanitarian goods getting to the people of Gaza as a success,” he said. “It is something additional that otherwise would not have gotten there when it got there. And that is a good thing.”

The Pentagon said on Thursday that 8,100 metric tons of aid had been delivered to shore using the pier since the operation started on May 17.

It was never meant to be more than a stopgap measure while the Biden administration pushed Israel to allow more food and other supplies into Gaza through land routes, a far more efficient way to deliver relief. But even the modest goals for the pier fell short, some American military officials say.

In recent weeks, Israel has given relief organizations greater access to Gaza, but the groups say the situation remains dire in much of the enclave.

The question of excess deaths in Gaza was raised in a letter published last week in the medical journal The Lancet, in which three researchers attempted to estimate how many people had died or would die because of the war, on top of the deaths reported by the Gaza Health Ministry. The letter immediately generated debate, with other researchers arguing for caution in any such projection.

One reason to be careful, those researchers said, is that any estimate of excess deaths would rely on data from Gaza’s health sector, which has been devastated by the conflict. Another reason, they said, is that it is hard to predict how epidemics and hunger, two threats to human life that can be triggered by war, will evolve. And Israel has not permitted researchers to enter the enclave since the start of the war last October.

The letter in The Lancet, which said that counting indirect deaths in Gaza was “difficult but essential,” based its estimate on looking at previous studies of recent conflicts, which indicated that three to 15 times as many people died indirectly for every person who had died violently. Applying what they called a “conservative estimate of four indirect deaths per one direct death,” the authors wrote that it was “not implausible” to estimate that about 186,000 deaths could eventually be attributable to the conflict in Gaza.

The letter, which The Lancet said had not been peer-reviewed, as is the case with other letters it publishes, provoked a significant response. The Board of Deputies of British Jews, which represents the Jewish community in Britain, said that the estimate was “little more than conjecture.”

Col. Elad Goren, an official with COGAT, the arm of the Israeli military that implements policy in Gaza, sidestepped a question about excess deaths.

Salim Yusuf, a cardiologist and epidemiologist in Canada who co-wrote the letter, said in an email that the estimate was based on studies of past conflicts and acknowledged that, “inevitably, these are projections.” “The point is that the real numbers of dead will be very large,” he said.

Michael Spagat, a professor of economics at Royal Holloway College at the University of London, who has written about the toll of the war in Gaza, wrote in an analysis that the letter “lacks a solid foundation and is implausible.” He argued that the authors had compared Gaza with a small and unrepresentative sample of other conflicts, and that conditions in Gaza, a small territory under intense international attention, are unique.

In an interview, Mr. Spagat cited other reasons to be cautious when discussing excess deaths in Gaza. He said that fears of major outbreaks of infectious diseases such as cholera have yet to materialize and that, although humanitarian agencies are warning of catastrophic levels of hunger, there is little evidence of widespread deaths because of starvation.

Still, Mr. Spagat said that it was “fair to call attention to the fact that not all of the deaths are going to be direct violent ones.”

The letter in The Lancet is not the first effort to quantify the human toll in Gaza beyond the figures reported by Gazan health authorities.

In February, epidemiologists at Johns Hopkins University and the London School of Hygiene and Tropical Medicine produced a model showing three different war scenarios affecting overall deaths in Gaza. They projected that if fighting and humanitarian access remained at the same levels, there could be an additional 58,260 deaths in the six months from March through August. Around 9,000 deaths have been directly attributed to the war since then by Gaza’s health ministry.

The health ministry says that more than 38,000 people have died in Gaza since Oct. 7, when Hamas, which controls the territory, led an attack on Israel in which 1,200 people were killed. While the ministry’s tally is broadly accepted, there remain questions about its methodologies and record keeping, as well as contradictions between its statements and underlying data. Most civilian victims, the ministry says, are women and children. But the figures do not distinguish between civilians and combatants.

The subject of excess deaths is sensitive because it touches on the collateral cost of Israel’s war against Hamas. On top of the large death toll, the attacks have damaged hospitals and shelters. Aid officials say that Israel has also restricted access to the fuel that medical facilities need to operate. Israeli officials say they do all they can to spare civilians, but blame Hamas for placing its forces in urban centers and civilian facilities. They have also said that aid agencies’ logistical difficulties, rather than Israeli restrictions, are to blame for the limited amount of humanitarian aid that is getting to Gazans.

Before the war, Gaza’s health sector produced reliable data, which helps in modeling excess deaths, but lack of access to Gaza for researchers makes the task more difficult, according to Zeina Jamaluddine, an epidemiologist at the London School of Hygiene and Tropical Medicine.

Gabby Sobelman contributed reporting.

President Biden halted the shipment in the spring to prevent the U.S.-made weapons from being used in Israel’s assault on the city of Rafah, in southern Gaza. It was the first time that Mr. Biden tried to influence Israel’s approach to the war by using his power to curtail arms.

The United States will continue to withhold 2,000-pound bombs out of concerns over the civilian deaths or injuries that they could cause in Gaza, the official said. A New York Times investigation in December found that American 2,000-pound bombs were responsible for some of the worst harm to Palestinian civilians since the war in Gaza began after Hamas attacked Israel on Oct. 7.

The news that some of the shipment would be released was earlier reported by The Wall Street Journal and Axios.

Israel’s defense minister, Yoav Gallant, alluded to the U.S. decision on the bombs on Thursday in a statement from his office that summed up a meeting with Brett McGurk, the top White House official for Middle East affairs. During their meeting on Wednesday in Tel Aviv, Mr. McGurk updated Mr. Gallant “regarding the delivery of critical munition, some of which will be sent to Israel in the coming days,” the statement said.

When Mr. Biden held up the shipment, he had been under pressure to limit or halt all arms shipments to Israel, something he had refused to do because of his strong support for the effort to destroy Hamas.

In the first two weeks of the war, roughly 90 percent of the munitions Israel dropped in Gaza were satellite-guided bombs of 1,000 to 2,000 pounds, according to a senior U.S. military official. The rest were 250-pound small-diameter bombs.

Analysts note that while smaller bombs have less explosive power than the 2,000-pound bombs, they can still cause significant injury and death, especially in areas with little protection, like tent camps.

The 250-pound GBU-39, which is also American-made, has increasingly become the weapon of choice for the Israeli military. Two of them were used in a deadly strike on a tent camp in Rafah on May 26 that Gazan health authorities reported killed 45 people.

Mr. Miller encouraged Israel “to take immediate steps” to hold the same individuals and entities accountable. “In the absence of such steps, we will continue to impose our own accountability measures,” he added.

The foreign ministers of the Group of 7 also issued a statement on Thursday condemning the Israeli government for recent moves to legalize five unauthorized Jewish outposts and other moves to expand its hold on the territory that is home to about 2.7 million Palestinians.

The far-right government of Prime Minister Benjamin Netanyahu of Israeli is unlikely to be moved by the international pressure. Expanding Israel’s hold over the West Bank is a goal of many ministers in his coalition, notably the finance minister, Bezalel Smotrich, a settler activist who recently secured approval to legalize the Jewish outposts that the Group of 7 denounced.

Mr. Smotrich had been withholding tax funds that Israel collects on behalf of the Palestinian Authority, which administers roughly 40 percent of the West Bank. In late June, he struck a deal with Israeli ministers to release a fraction of the funds in exchange for the legalization of the five unauthorized communities.

In its statement, the Group of 7 foreign ministers criticized Mr. Smotrich specifically and the arrangement he had made for the additional settlements, as well as a recent Israeli government announcement that it would designate more than 3,000 acres of land in the West Bank as “state lands” and plans to expand existing settlements with nearly 5,300 new housing units.

“The Government of Israel’s settlement program is inconsistent with international law, and counterproductive to the cause of peace,” the leaders wrote.

Israel seized control of the West Bank from Jordan in a war in 1967, and Israeli civilians have since settled there with both the tacit and explicit approval of the Israeli government, living under Israeli civil law while their Palestinian neighbors are subject to Israeli military law. The international community largely views the Israeli settlements as illegal, and many of them are illegal under Israeli law, too, but they are often tolerated by the government and sometimes subsequently legitimized.

Palestinians have long argued that the Israeli settlements are a creeping annexation that turns land needed for any independent Palestinian state into an unmanageable patchwork.

That is the stated intent of Mr. Smotrich and his allies in the government. When Mr. Smotrich released some of the revenue he was withholding, he said he was meeting with planning authorities about building new housing for Jewish people in the territory. “We’re building the good country and thwarting the creation of a Palestinian state!” he said on social media.

The release of the funds relieves some of the financial pressure on Palestinian officials, but tensions in the West Bank are high, and violent confrontations between settlers and Palestinians have been on the rise.

The United Nations Office for Coordination of Humanitarian Affairs tracks violence in the West Bank on a weekly basis, and has documented more than 1,000 Israeli settler attacks against Palestinians since October, when the war in Gaza between Israel and Hamas began.

The latest update from the agency on Wednesday noted that in the previous week there had been 22 settler attacks on Palestinian property, including hundreds of olive trees. One Palestinian family was displaced by a settler attack in Hebron. Armed settlers raided a herding community and set fire to fields for grazing, also near Hebron, and settlers believed to be from Evyatar — one of the five outposts that Mr. Smotrich secured legalization for — attacked a Palestinian farmer in Nablus, threatening him not to return to his land.

The U.S. sanctions are aimed at curbing some of that violence. Among those targeted are the two co-founders of Tsav 9, a group of extremist settlers who have tried to block aid convoys to Gaza, and Lehava, a nonprofit that U.S. officials called “the largest violent extremist organization in Israel” with 10,000 members. The list also includes four farms that have encroached on Palestinian lands or obstructed Palestinian access to land.

Reut Ben Haim, one of the co-founders of Tzav 9 who were sanctioned on Thursday, responded with defiance.

“The imposed sanctions are an anti-democratic intervention,” she said in a statement that called on the Israeli government to “protect all of its citizens, both in legal protection and in security protection.”

“Hamas is negotiating on its own behalf and on behalf of the entire resistance axis, and what Hamas accepts, we accept,” Mr. Nasrallah said in a televised speech.

Israeli forces and Hezbollah fighters in Lebanon, who are backed by Iran, have traded fire since the war in Gaza began after Hamas led an attack on Israel on Oct. 7. About 150,000 people in northern Israel and southern Lebanon have fled their homes because of the fighting, and world leaders are worried that continued hostilities could quickly spiral into a full-fledged war that further destabilizes the already fraught region.

Mr. Nasrallah, in his speech, referred to these concerns, noting that “many delegations” from the international community have visited Lebanon to discuss defusing tensions. “We repeated the same words: If you want to stop the northern front, stop the fire in Gaza,” he said.

But the cease-fire talks have been halting, and the fighting between Israel and Hezbollah — cross-border attacks with drones, rockets and airstrikes — has escalated in recent weeks, heightening fears that a wider war may be imminent.

On Tuesday, two Israelis — Noa and Nir Baranes, a married couple from Kibbutz Ortal in the northern Golan Heights — were killed in a Hezbollah strike on their car that the Lebanese armed group said had targeted an Israeli military base in response to an earlier Israeli “assassination” of a Hezbollah figure in Syria. The civilian deaths put additional pressure on the Israeli government to address tensions with Hezbollah, even as the Israeli military keeps returning to parts of Gaza it had previously considered pacified to suppress a resurgence of Hamas fighters.

The Israeli military said on Wednesday that its air force struck a “military site” in southern Lebanon after soldiers identified several Hezbollah operatives entering it, and that it also had targeted other Hezbollah sites nearby. Israeli government officials and military leaders have in recent weeks toured northern Israel and met with troops stationed there who were preparing for a potential escalation.

Israel has invaded Lebanon three times in the last 50 years, most recently in 2006, when the sides fought a monthlong war that killed more than 1,000 people in Lebanon, mostly civilians, and more than 150 in Israel, mostly soldiers.

Yoav Gallant, Israel’s defense minister, has said that a diplomatic solution to the conflict with Hezbollah is preferable. But he has also emphasized, including in talks with his U.S. counterpart, Lloyd J. Austin III, in Washington late last month, that Israel is “determined to establish security” in the north and change “the reality on the ground.”

Israeli security experts are concerned that a war against Hezbollah will be more intense — and more likely to draw in other players — than the fight against Hamas.

A new report from Tel Aviv University’s Institute for National Security Studies warned that “Hezbollah has the military capabilities to conduct an exceedingly protracted war, probably lasting many months, and cause severe damage to Israel” and that it could turn into “a multi-front war against Iran and its other proxies.”

The report, led by the retired Israeli Brig. Gen. Meir Elran, a senior researcher at the institute, said “there is a growing sense of futility regarding the future of the northern border.” It also noted that “public discourse has been heavily focused on the possibility of a comprehensive war with Hezbollah.”

Comprehensive war is precisely what France, the United States and others have been hoping to prevent with diplomatic visits to the region. Whether efforts at de-escalating the conflict between Israel and Hezbollah can succeed may well depend on how the cease-fire talks in Qatar progress.

On Wednesday, the C.I.A. director, Mossad chief and Egyptian intelligence head met in Qatar with the Qatari prime minister in an effort to find a peace formula both Israel and Hamas can agree on. (Egypt and Qatar have been relaying proposals to Hamas leaders.)

So far, however, Israel and Hamas disagree over a fundamental question: whether the cease-fire will be permanent or just a temporary pause to allow for an exchange of hostages taken from Israel for Palestinian prisoners.

The talks have been “progressing positively,” said Majed al-Ansari, the spokesman for Qatar’s Foreign Ministry, before the latest gathering. But, he added, “We are by no means out of the woods.”