Hours after he arrived in Al-Mawasi, Mr. Aborjela said, shelling from tanks reached tents people were sheltering in.

“The tanks got close to us,” he said. “And they started shelling the people even though it is supposed to be a safe zone.”

The Israeli military said that it “takes feasible precautions to mitigate civilian harm” when asked whether its ground forces opened tank fire toward Al-Mawasi.

In a statement, the Israeli military said Thursday that its forces had “intensified their operational activities in the area” of Deir al Balah, after its intelligence indicated the presence of Hamas infrastructure and fighters there and in Khan Younis.

Dr. Iyad al-Jabri, a surgeon and administrator at the Al-Aqsa Martyrs Hospital in Deir al Balah, said that seven people who were wounded from the shelling of Al-Mawasi were brought to the medical facility.

They weren’t the only ones hurrying to the hospital. Hundreds of families fleeing the new evacuation orders arrived there to take shelter, even as hospital officials began to make their own contingency plans in case the Israeli military further expands its evacuation zones to include the hospital.

“In this area there is a ground invasion and we have to think, ‘Where can we go, what are we going to do?’” Dr. al-Jabri said. “So we are running around seeing where can we send our patients in case, God forbid, we are ordered to leave this hospital.”

More than 150,000 displaced people have been living in the central Gaza areas subject to Wednesday’s evacuation order, according to the United Nations. Nearly a dozen such orders issued this month by the Israeli military have so far affected an estimated 250,000 people and disrupted the movement of aid, the United Nations said. The multiple orders to flee between Aug. 8 to 17 have caused the loss of essential health services for many, the United Nations said, affecting 17 health facilities in total.

Before the orders issued this month, the United Nations had already estimated that around 90 percent of Gaza’s population of more than two million people had been forced to leave their homes since the war began because of evacuation orders, Israeli bombardments and ground fighting.

In a statement, the Gaza Health Ministry said that Israel’s military offensive was approaching the vicinity of Al-Aqsa hospital, and called on the international community and the United Nations to protect the overcrowded complex.

The Israeli military said on Wednesday that it had been “made clear” to hospitals that they did not need to evacuate, but did not respond to questions about which hospitals this was communicated to and how.

Israel has accused Hamas of taking advantage of Gaza’s urban terrain to provide its fighters and weapons with an extra layer of protection, including running tunnels under neighborhoods and launching rockets near civilian homes. Hamas denies these accusations and says its members are Gazans who live among the population.

International law experts have said that no matter what, Israel bears a responsibility to protect civilians. U.S. officials, while backing Israel’s assertions, have also called for Israel to do more to safeguard Gazans.

Majdi Nassar, 33, a taxi driver before the war who fled to Deir al Balah from the northern Gaza Strip, received a call last Friday on his cellphone instructing him to leave, because the Israeli military said the neighborhood blocks they were in “had become fighting zones.”

“We were 10 people, my wife, son and in-laws,” he said. “We were all sharing one tent and had to dismantle it and flee. We took everything with us: the tent and the canned food we had and our clothes.”

It was the eighth time they have had to flee over 10 months of war.

“I don’t know what they are attacking here now,” he said. “I didn’t hear or see any shooting, or rockets, or anything from the Palestinians in this area.”

He said he was fleeing only for the safety of the children with him.

“I myself no longer care,” he said. “Death is no longer the worst scenario. This life is much worse. The scene of thousands of people running for their lives every day is unbearable.”

The autopsy reports have not been made public. The New York Times has not reviewed them and cannot confirm the results.

Four other bodies found in the tunnels near the hostages, believed to belong to Hamas militants, did not display the same marks, the military spokesperson said.

How and when the hostages died has been a matter of contention. Hamas has blamed the deaths on Israeli airstrikes, and the Israeli military has acknowledged some of them likely died while Israel was carrying out military operations in the area where they were found. Some Israel news outlets reported the hostages may have suffocated when the tunnel filled with toxins after an airstrike.

The revelations raise new questions about the circumstances of the hostages’ deaths after months of conflicting statements about some of the recovered captives from Hamas and the Israeli military.

On Tuesday, the Israeli military announced that it had recovered the six bodies in a hidden tunnel network, alongside four of their presumed captors.

Five of the six captives were already believed to be dead, according to the Israeli military. Three of them — Haim Peri, 80; Yoram Metzger, 80; and Alexander Dancyg, 75 — had been abducted from the Nir Oz kibbutz near the Gaza border. Two others — Nadav Popplewell, 51, and Yagev Buchshtab, 35 — were taken from another border community, Nirim.

The sixth body belonged to another resident of Nir Oz, Avraham Munder, 79. Mr. Munder’s death had not been established previously.

Abu Ubaida, a spokesman for Hamas’s military wing, said in March that Mr. Metzger and Mr. Peri were among seven hostages who had been killed in Israeli airstrikes in Gaza. Hamas then said in May that Mr. Popplewell had died from injuries sustained in an Israeli airstrike more than a month earlier.

Weeks later, in early June, the Israeli military’s chief spokesman, Rear Adm. Daniel Hagari, said that it was examining the possibility that some of the hostages had been killed together months earlier while Israeli forces were operating in the Khan Younis area.

On Tuesday, Adm. Hagari was asked again about how the hostages died at a news conference. He repeated what he had said in June — that the “hostages were killed while our troops were operating in Khan Younis” — and added that a forensic examination would reveal more.

Israeli news media reported on Tuesday that initial assessments suggested that five of the six hostages had died from suffocation when an Israeli airstrike hit another tunnel, causing the one they were in to fill with carbon dioxide. The Times could not confirm those reports.

The recovery of six dead hostages this week emphasized the urgent need for a cease-fire deal, families of the captives said in their statement on Thursday. The forum said the evidence the hostages may have been shot “serves as further proof of the cruelty of the terrorists,” and it condemned the government’s failure to reach a cease-fire agreement that would lead to the return of all hostages and an end to the fighting in Gaza.

“In every minute that the deal is not completed, another hostage could lose their life,” the forum said. “After 10 and a half months of war in which the hostages have been suffering, tortured, and dying, it is clear to all that the return of the hostages is only possible through a deal.”

An Israeli delegation led by David Barnea, the head of Israel’s Mossad intelligence agency, and Ronen Bar, who leads the Shin Bet domestic security service, was heading to Cairo on Thursday to continue talks, said Omer Dostri, the Israeli prime minister’s spokesman.

Brett McGurk, the White House coordinator for the Middle East and North Africa, was already in Cairo on Thursday and William J. Burns, the C.I.A. director, was also expected to attend the talks, according to a Western official who spoke on condition of anonymity.

The deliberations in Cairo were expected to focus on security arrangements along Gaza’s border with Egypt and on reopening the Rafah border crossing between Gaza and Egypt, said an Israeli official and another official familiar with the matter. Both spoke on condition of anonymity because they were not authorized to speak publicly.

One main focus of disagreement between Israel and Hamas has been Mr. Netanyahu’s insistence on maintaining an Israeli military presence along the Philadelphi Corridor, a narrow strip of land along Gaza’s southern border with Egypt. The Israeli leader has argued that the area has served as a major conduit for weapons smuggling into Gaza and that abandoning it would allow Hamas to quickly rearm.

Egypt and Hamas strongly object to continued Israeli control of the corridor and have called for a full Israeli withdrawal from Gaza. Israeli security officials have suggested that other solutions can be found.

A visit to the region this week by Secretary of State Antony J. Blinken ended without any apparent resolution to major sticking points — and in acrimony, with Mr. Netanyahu and Hamas officials trading blame for obstructing progress.

Israeli negotiators were taken aback and, in some cases, angered by Mr. Blinken’s statements this week apparently affirming that Mr. Netanyahu had accepted the American bridging proposal and that it was now up to Hamas to follow suit, according to people familiar with the talks.

Those statements — which came after a nearly three-hour meeting on Monday between Mr. Blinken and Mr. Netanyahu — made it appear that the Israeli prime minister and the Biden administration saw eye-to-eye on aspects of the proposal that Hamas clearly would not accede to, one of the people said, dimming the prospects of an agreement. Instead, they said, Mr. Blinken could have called more vaguely for flexibility on both sides.

But the Western official disputed that interpretation, saying that Mr. Blinken was clear that there were a lot of details left to be ironed out.

“These are still complex issues, and they’re going to require hard decisions by the leaders,” Mr. Blinken said after the meeting.

The details of the bridging proposal have not been made public. Another Israeli official with knowledge of the talks, who was not authorized to speak about them publicly, cautioned that few people really know what is being said behind closed doors, and said that talks were continuing at various levels as part of a difficult negotiation.

Rawan Sheikh Ahmad and Aaron Boxerman contributed reporting from Jerusalem.

The tanker, the Sounion, was sailing about 90 miles west of the Yemeni port of Hudaydah early on Wednesday when two small boats approached it, said a statement on social media from Britain’s maritime trade agency, which is based in Dubai.

“The first craft had three to five persons onboard while the second had approximately 10,” the statement said. “The two small craft hailed the merchant vessel, leading to a brief exchange of small-arms fire.”

The small craft retreated and the ship was then hit by three “unidentified projectiles,” starting a fire and causing the ship to lose engine power, it said. It was not clear on Thursday whether the fire had been extinguished.

The crew was rescued by a ship from an E.U. military mission, Operation Aspides, that has been mounted in response to attacks by the Houthi militia, according to a statement the mission posted on social media Thursday.

The statement included a photograph showing an enclosed lifeboat, typical in the oil industry, bobbing in the water and a second photo of crew members aboard a rescue speedboat.

After coming under attack, the ship’s captain called for help. The E.U. military destroyed what it described as an “unmanned surface vessel” that had posed an imminent danger to the Sounion. The crew was being transported to Djibouti, the statement said.

The Houthi militia, which is backed by Iran, began firing late last year on ships entering the Red Sea en route to the Suez Canal, which is a vital artery for vessels moving between Asia, Europe and the eastern United States.

The United States and Britain have launched strikes against the Houthis in response, but analysts have said they have done little to damage the militia’s military infrastructure. The attacks have continued, forcing ships to find alternative routes and disrupting global trade. Oil prices on Thursday were little changed, trading near their lowest levels of the year.

Over the course of dozens of attacks, at least two vessels have sunk and at least three crew members have been killed.

Jason Karaian contributed reporting.