Videos offer glimpses of the battle for Gaza.

Discussions have been underway for Hamas to release a small number of hostages, including some Americans. Proposals have shifted in recent days, but the discussions on Wednesday and early Thursday revolved around a proposal for Hamas to release 10 to 15 prisoners. They would include some Americans and other foreign nationals taken by Hamas on Oct. 7, as well as Israeli women, civilians and children, an official said.

Hamas has asked for a three-day pause in the fighting across Gaza.

On Thursday, Mr. Burns had a group meeting with David Barnea, the chief of Mossad, the Israeli intelligence service, and Mohammed bin Abdulrahman bin Jassim Al Thani, the prime minister and foreign minister of Qatar, the officials briefed on the meeting said.

Mr. Burns also had separate meetings with the emir of Qatar, Sheikh Tamim bin Hamad Al Thani, and with the country’s intelligence chief, an official said.

Mr. Burns did not meet directly with Hamas officials, according to people briefed on the talks.

One official described the talks as positive and said good progress had been made.

While U.S. officials have not confirmed details of the proposal, they have publicly endorsed the idea of releasing hostages in exchange for a temporary pause in hostilities.

In recent days, American officials, including Antony J. Blinken, the secretary of state, who was in the Middle East last week, have intensified their push for “humanitarian pauses.”

U.S. officials and others briefed on the discussions said Hamas had previously made an offer to release a group of hostages. Those conversations took place right before the Israeli military entered Gaza. But Israeli officials doubted Hamas’s sincerity and went ahead with their ground operation.

U.S. officials said discussions continued even after Israeli forces surrounded Gaza City.

Qatar has been deeply involved in the hostage negotiations. The political leaders of Hamas have offices in Doha and live part-time there and part-time in Turkey. The Qatari government has regular discussions with Israel, Hamas and the United States.

In one video released Wednesday by Hamas of what it claims is fighting with the Israeli military in Gaza City, young men can be seen firing rocket-propelled grenades and guns while scrambling for cover in piles of debris between ruined buildings.

Hamas also released a compilation video on Tuesday showing its fighters targeting Israeli Defense Forces. One clip, which has been geolocated by The New York Times, shows Hamas fighters engaging in a gunfight battle in Beit Lahia in northern Gaza. It is not clear exactly when the video was filmed, but satellite imagery taken on Oct. 30 by Planet Labs, a commercial satellite company, showed dozens of Israeli tanks or armored vehicles in the area where the video was filmed.

Israeli ground forces moved into Gaza late last month after weeks of airstrikes launched in retaliation for the Oct. 7 attack by Hamas. Armored columns and troops of infantry have since advanced deep into the enclave, bisecting the strip and penetrating the heart of Gaza City in what Israel says is a campaign to destroy Hamas and the network of tunnels from which it fights.

Israeli soldiers could be seen bulldozing and blowing up tunnel entrances in a video posted Thursday by the Israeli military on X, formerly Twitter. The video also shows the interior of a tunnel with concrete walls, and at one point a soldier points out a bank of car batteries connected to an inverter that he says are used to help power air filtration systems.

“Water and oxygen storage discovered inside the tunnels indicates Hamas’s preparations for prolonged stays underground,” the military said in its post. It said 130 tunnel entrances had been destroyed since the beginning of the war.

The fighting has sent tens of thousands of desperate men, women and children — some waving white flags — streaming south in search of a safe haven. On Wednesday, thousands packed whatever they could carry and set off down Salah al-Din Road, the Gaza Strip’s main north-south route, after Israel announced a five-hour pause in fighting along the road.

Some of those fleeing said they had begged Israeli soldiers to allow them to take their vehicles but were told they had to walk.

“Nonstop bombing all the time. Today many left because of the bombing. There are many tanks on the roads,” said Mansour Shatatez, who spent hours walking from Beit Hanoun in the strip’s far north.

“There are bodies, decomposed bodies dumped in the middle of the road,” he said in an interview. “People stepped over the bodies and kept walking.”

Israel was also striking targets in the enclave’s south, according to officials from the Hamas-run government. The Gazan health ministry said on Thursday morning that 241 people had been killed throughout Gaza “during the past hours,” nearly half of them in southern Gaza.

Hwaida Saad contributed reporting.

“We have been told by the Israelis that there will be no military operations in these areas over the duration of the pause and that this process is starting today,” John F. Kirby, a spokesman for the White House, said in a statement. Each pause will be announced three hours in advance, he said, and a second safe corridor along the coastal road will be opened for evacuations.

Asked about the White House announcement, Prime Minister Benjamin Netanyahu’s office said in a statement: “Israel is permitting safe passage corridors from the northern Gaza Strip to the south.” It added that 50,000 Gazans had taken that route on Wednesday alone.

But “the fighting is continuing and there will be no cease-fire until our hostages are released,” the statement added. “We again call on the civilian population in Gaza to evacuate to the south.”

Mr. Biden said he asked Mr. Netanyahu during a call on Monday to pause its assault on Hamas, which would allow more civilians to flee the fighting and possibly facilitate the release of more than 200 hostages, including a handful of Americans.

“I’ve asked for a pause longer than three days,” Mr. Biden told reporters on Thursday before leaving for a domestic policy trip to Illinois. Asked if he was frustrated that Mr. Netanyahu took so long to agree, the president hinted at some impatience. “It’s taken a little longer than I hoped,” he said. As for the fate of the hostages, he said, “We’re still optimistic.”

But Mr. Biden has not joined the calls by some in his party and around the world for a full cease-fire, reasoning that Israel has a legitimate interest in destroying Hamas after its Oct. 7 terrorist attack killed more than 1,400 people. He ruled out the prospect of a cease-fire again on Thursday, saying: “None. No possibility.”

Since mid-October, more than 33,500 cases of diarrhea have been reported, more than half of them among children younger than 5, the group said. Before the war, there were on average 2,000 monthly cases of diarrhea among children of that age, according to the organization.

The risk of uncontrolled disease outbreaks compounds the calamitous humanitarian situation in Gaza, where thousands have been killed, according to Gazan health officials, and aid agencies warn that 1.5 million people are homeless and many are living with acute shortages of food and water one month into the war.

In recent weeks, nearly 9,000 cases of scabies and lice, more than 12,600 cases of skin rash and nearly 55,000 cases of upper respiratory infections have proliferated in densely packed Gaza, where hundreds of thousands of displaced people have crammed into United Nations-run shelters, the W.H.O. said.

With fuel and medicine running dry, Gaza’s health care system is collapsing. Doctors are being forced to stretch paltry resources to treat the sick and injured and make impossible choices on who lives and who dies. The lack of fuel has led to water treatment plants shutting down and all solid waste collection being halted, creating conditions primed for the spread of infectious diseases, health officials say.

The United Nations office on humanitarian affairs said that by Thursday, all of the Gaza Strip’s 120 municipal water wells were expected to shut down as fuel is depleted. Water entering through the border with Egypt on aid convoys is only 4 percent of what is needed, the office said in its daily update.

Shelters run by UNRWA, the U.N. agency that aids Palestinian refugees, are so overcrowded that an average of 160 people are sharing a toilet and there is one shower for every 700 people, according to the United Nations.

On Thursday morning, Israeli troops raided Jenin’s refugee camp and withdrew before returning again later in the day, engaging in hourslong gun battles with Palestinian militants, according to Jenin’s acting governor, Kamal Abu al-Rub. The Israeli military confirmed that troops were operating in the city but declined to immediately provide further details.

The West Bank — where millions of Palestinians under Israeli military occupation live uneasily alongside hundreds of thousands of Israeli settlers — has long been seen as a powder keg. Over the past year, Palestinian militants have increasingly defied both Israel and the Palestinian leadership in Ramallah, opening fire on Israeli soldiers and civilians.

In July, Israel conducted a two-day operation in Jenin to clear out Palestinian militants who had entrenched themselves. At least 12 Palestinians and one Israeli soldier were killed in the fighting, which included rare Israeli airstrikes in the city.

The Hamas-led massacres on Oct. 7 and Israel’s campaign in Gaza prompted a renewed surge of violence in the West Bank. The Israeli military said Tuesday that over 1,350 Palestinians had been arrested throughout the West Bank since the beginning of the war, including over 870 belonging to Hamas.

On Wednesday night, Prime Minister Benjamin Netanyahu of Israel said authorities had moved aggressively since the war’s start to stop Palestinian militant activity in the West Bank. Israel sought “to prevent an escalation and the transformation of Judea and Samaria into a second front,” said Mr. Netanyahu, using the Hebrew name for the territory.

The nightly raids by Israeli troops in Palestinian cities have ended in firefights or even Israeli airstrikes. U.S. officials, including President Biden, have said Jewish extremist violence against Palestinians in the West Bank presents another potential flashpoint.

At the same time, the brutal videos emerging from Gaza, such as those of dead and wounded civilians flooding local hospitals, have shocked the area’s Palestinian residents, said Mr. Abu al-Rub, the Jenin acting governor.

“There’s constant tension, constant anxiety. The economic situation has plummeted, and feelings are running high,” he said. “People’s sense of safety has been broken” by the increased Israeli raids, he added.

“Civilians must be protected,” he said. “That is not negotiable.”

Mr. Macron said France would increase its aid for civilians in Gaza to 100 million euros for 2023, and he encouraged other countries to give more as well. The United Nations said last week that it needed $1.2 billion to fund humanitarian efforts for Palestinians in Gaza and the Israeli-occupied West Bank through the end of the year.

Mr. Macron opened his remarks with a call to immediately and unconditionally free hostages held in Gaza, mostly by Hamas, which has been the governing power there since 2007, and he said Israel had every right to defend itself. But he reiterated that “the fight against terrorism can never go without rules” to avoid civilian casualties.

“The suffering of Israelis is now joined by that of Palestinians, and we cannot accept that, because all lives are equal,” he said. “There is no double standard.”

International organizations and aid groups at the conference said urgent needs in the territory far outstripped the little supplies and fuel that have trickled in so far.

An Israeli siege in response to the Oct. 7 attacks by Hamas kept food, water and medicine from entering the enclave until recently. Many civilians fear for their safety, even in U.N.-run shelters, some of which have been damaged in Israeli strikes.

“Our shelters are overcrowded, with little food, water or privacy,” Philippe Lazzarini, the commissioner-general of UNRWA, the U.N. agency that helps Palestinian refugees, said at the conference. “The appalling sanitary conditions represent a looming public health hazard.”

“Outside the shelters, entire neighborhoods have been leveled, extinguishing countless lives, hopes and dreams,” he added.

Mr. Lazzarini and other officials said more entry points into Gaza were needed to create a “meaningful and continuous flow of humanitarian aid.” The only Gaza border crossing in operation is the Rafah crossing to Egypt.

Participants at the conference — which was hastily convened on top of a separate, long-scheduled meeting, the Paris Peace Forum — are also expected to discuss how to secure the release of hostages held in Gaza.

Mr. Macron spoke on Tuesday with Prime Minister Benjamin Netanyahu of Israel, and French officials have been coordinating the conference’s agenda with their Israeli counterparts. But Israel, which has rebuffed calls for a cease-fire or a “humanitarian pause,” did not send a representative.

Also in attendance were officials from the International Committee of the Red Cross, along with top European Union officials and several senior European leaders. The Palestinian Authority, which administers part of the West Bank, and the United States were also represented.

The soft-spoken Mr. Ajami is one of roughly 15 archaeologists, with experience in excavations ranging from ancient scrolls to buried tombs, who have mobilized to try to provide closure for Israelis still awaiting news of their loved ones. The team has recovered the remains of at least 60 people so far, he said, most of them in Be’eri, a village of 1,000 people that suffered devastating losses in the attack.

The Oct. 7 assault left approximately 1,400 dead, 240 abducted and scores missing in Israel. The country is still reeling, with thousands evacuated from their homes, and a lagging government response. Weeks after the disaster some bodies have yet to be identified and their families remain in the dark.

Israeli health officials accustomed to handling a few dozen cases per week have been overwhelmed by the influx of bodies, some of which, they say, were desecrated or burned. While the military is leading the identification efforts, a handful of organizations and independent initiatives — ranging from groups of bird watchers to K-9 units — are combing the affected area looking for traces of the missing.

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Yossi Cohen, a reserve colonel overseeing the effort to identify the missing, went to what remained of Ram and Lili Itamari’s home in the southern Israeli village of Kfar Aza on Oct. 15. The visit prompted him to call the head of the Antiquities Authority and ask for archaeological assistance, he said.

As Hamas gunmen stormed the village, Lili Itamari, 63, told her family that she had hidden herself in a reinforced safe room, said her son Tomer. As in other border villages, militants set the house ablaze and when the military finally arrived at Ms. Itamari’s home, they could not find any trace of her.

“I realized that with over 200 people missing, and tens of burnt buildings and bodies, we need to approach this search differently,” said Colonel Cohen.

The next day, Mr. Ajami and a team began searching Ms. Itamari’s house. In the weeks since, the archaeologists have sifted through other razed homes near the Gaza border, looking for even minute slivers of bone and teeth.

“In some ways, this work resembles our everyday practice,” Mr. Ajami said, including the use of standard equipment like sifting screens and dustpans. “But it’s also very different. The bones we usually find belong to faceless people who died thousands of years ago.”

Digging through the remains of Ms. Itamari’s home, the archaeologists found small remains that they sent for DNA analysis, allowing authorities to identify her, her son said. In another case in Be’eri, the teams uncovered teeth and blood tissue in a carpet, Mr. Ajami said.

On Monday, Colonel Cohen stepped into a burned home in Be’eri. Inside, an archaeologist and a soldier knelt in a large pile of ashes, brushing the remains into a bucket for examination.

The teams can still find remains after a person has already been buried. An Israeli military official said that in such cases, they are placed in the grave, without informing the families.

For the first week after the attack, Joe Uziel, an expert on the Dead Sea Scrolls — a collection of ancient Jewish manuscripts — sat at home “feeling helpless,” he said. When the military called for his help, he signed up.

“We do have a unique set of skills that is applicable,” Dr. Uziel said. “It’s comforting to know that I’m contributing something.”

The downing of a Reaper drone, the mainstay of the American military’s aerial surveillance fleet, was the latest escalation of violence between the United States and Iran-backed groups in Yemen, Iraq and Syria. The episodes have underscored the risks that the conflict between Israel and the Palestinian group Hamas could spiral into a wider war.

On Oct. 19, a U.S. Navy warship in the northern Red Sea shot down four cruise missiles and more than two dozen drones launched from Yemen that the Pentagon said might have been headed toward Israel.

Yemen’s Houthi militia claimed it had attempted an attack on southern Israel on Oct. 31, saying it had launched a “large batch” of ballistic and cruise missiles, as well as drones, toward Israeli targets. The Israeli military said its aerial defense system had intercepted a surface-to-surface missile fired toward Israel “from the area of the Red Sea.” It said it had also intercepted other “aerial threats” in the area, none of which entered Israeli territory.

The Defense Department said on Wednesday that there had been at least 41 attacks on U.S. forces in Syria and Iraq by Iran-backed militias since Oct. 17. At least 46 U.S. service members have been injured, 25 of whom suffered traumatic brain injuries, the Pentagon said.

Ms. Tlaib, the only Palestinian American in Congress, has said the slogan is “an aspirational call for freedom, human rights and peaceful coexistence, not death, destruction or hate.” Pro-Palestinian protesters used the slogan in a video Ms. Tlaib recently posted online that accused President Biden of supporting genocide in the Gaza Strip.

“When it comes to the phrase that was used, ‘from the river to the sea,’ it is divisive, it is hurtful, many find it hurtful and many find it antisemitic,” said Karine Jean-Pierre, the White House spokeswoman, on Wednesday. “We categorically reject applying that term to the conflict.”

The House passed a resolution Tuesday evening to censure Ms. Tlaib, a Democrat from Michigan, for embracing that phrase and “promoting false narratives” surrounding Hamas’s Oct. 7 attack on Israel that killed about 1,400 people, mostly civilians.

A video that Ms. Tlaib released Friday said that Mr. Biden “supported the genocide of the Palestinian people,” and she warned the president, who is from her own party, that “we will remember in 2024.”

A genocide is defined as the deliberate and systematic killing of members of a particular ethnic, national, racial or religious group in order to destroy that group. The Israeli military has said it is targeting Hamas, which carried out terrorist attacks on Israeli civilians, not the Palestinian people.

The White House did not comment on the video last week and on Wednesday Ms. Jean-Pierre declined to comment on the House’s censure.

“We respect that there are strong feelings about the war,” Ms. Jean-Pierre said. “We have expressed our views ourselves in public and in private conversations with Israeli officials.”

But, she added, “Remember, Israel is defending itself from terrorists.”

The censure resolution, which passed 234 to 188, with 22 Democrats voting in favor, cited Ms. Tlaib’s use of the phrase “from the river to the sea,” which the Anti-Defamation League deems antisemitic. The resolution called the phrase “a genocidal call to violence to destroy the state of Israel and its people to replace it with a Palestinian state extending from the Jordan River to the Mediterranean Sea.”

Kayla Guo contributed reporting.