Many also denounced Israel’s strike of a hospital complex on Monday that ignited fires that spread to a tent shelter for displaced people next to a hospital, leading to accounts that people were burned alive.

Some of the sharpest criticism came from Israel’s allies, including the United States, which vetoed three resolutions blocking efforts for a cease-fire in the first eight months of the war and abstained from one that eventually passed in June.

“There are no words, simply no words, to describe what we saw,” said Linda Thomas-Greenfield, the United States ambassador to the United Nations. “Israel has a responsibility to do everything possible to avoid civilian casualties, even if Hamas was operating near the hospital in an attempt to use civilians as human shields. We have made this clear to Israel.”

Ms. Thomas-Greenfield also said that a “policy of starvation” in northern Gaza would be “horrific and unacceptable and would have implications under international law and U.S. law.”

The rebuke came as the United States warned Israel on Sunday in a letter that if it did not provide scaled-up humanitarian aid to Gaza in the next 30 days, it would face repercussions that could include a halt to American military aid to Israel.

Riyad Mansour, the Palestinian envoy to the United Nations, accused Israel of trying to force Palestinians out of Gaza by withholding food aid, saying, “This is not war; these are crimes.” Mr. Mansour added: “This is genocide. They must be stopped, and they must be stopped now.”

Israel’s ambassador to the United Nations, Danny Danon, defended Israel’s actions and blamed Hamas for using Palestinian civilians as human shields and for robbing aid trucks.

“The only way to improve the humanitarian situation in Gaza is to defeat Hamas and completely disarm it,” Mr. Danon said. He claimed Hamas “steals, stores and sells the aid that enters the Gaza Strip and uses it to feed its terrorist machine and not to feed the Gazans.”

Scott Peterson, the Gaza director of UNRWA, the main U.N. aid agency for Palestinians, said on Wednesday that Israel had allowed 12 aid trucks into northern Gaza on Sept. 30, but no other trucks were allowed into that region of the enclave after that.

COGAT, the Israeli government agency that oversees policy in Gaza and the West Bank, insisted that it was not limiting aid to Gaza and has accused humanitarian agencies of failing to distribute the supplies it has admitted into the enclave after screening. On Wednesday, it said that it had inspected and permitted 50 aid trucks to enter northern Gaza from Jordan — carrying food, water, medical and other supplies — “in accordance with international law.”

To service civilians adequately, the United Nations said it needed about 40 to 50 trucks per day in northern Gaza and about 250 to 300 aid trucks per day in the south.

“The level of suffering in Gaza defies our ability to capture it in words, or even to comprehend its scale,” said Joyce Msuya, the U.N.’s acting humanitarian chief to the Council. “Reality is brutal in Gaza, and it gets worse every day, as the bombs continue to fall, as fierce fighting continues unabated and as supplies essential for people’s survival and humanitarian assistance are blocked at every turn.”

Ms. Msuya told the Council that Israel’s military on Monday had detained U.N. aid workers who were evacuating severely burned patients to other hospitals in Gaza, holding them up at checkpoints for hours and threatening the lives of the injured.

“Medical staff kept one child alive by hand-pumping oxygen for over seven hours until they made it through the checkpoint,” she said.

Mr. Danon did not respond to her comments when addressing the Council.

That is a small fraction of what aid agencies say is needed to offset a severe hunger crisis in Gaza, especially in the north, where Israel “has tightened a siege” this month, the United Nations has said, as it steps up military operations against Hamas.

“People have run out of ways to cope, food systems have collapsed and the risk of famine is real,” the U.N. World Food Program said this week, referring to northern Gaza.

On Sunday, Defense Secretary Lloyd J. Austin III and Secretary of State Antony J. Blinken sent a letter addressed to Israel’s minister of defense, Yoav Gallant, and its minister of strategic affairs, Ron Dermer, saying that Israel had 30 days to allow more aid into Gaza or the United States, Israel’s main military supplier, would consider cutting off military aid.

The letter, a copy of which was obtained by The New York Times, describes the humanitarian situation as “increasingly dire.” It also criticizes Israel’s government for halting commercial imports, preventing aid workers from moving from south to north Gaza, confining the population into a narrow coastal strip and for enabling a burdensome process of vetting what aid can enter the enclave.

Israel should enable a minimum of 350 aid trucks per day to enter, to allow people confined into a so-called humanitarian zone on the coast to move inland before winter and also take other measures, the letter said.

The letter appeared to depart from the United States approach of “hectoring” Israel’s government to allow more aid, according to Michael Hanna, U.S. program director for the International Crisis Group think tank.

As a result, it gives the administration “the possibility of having a really serious conversation” with Israel about aid. But, Mr. Hanna said, some policymakers in Israel would likely view its eventual outcome as an affirmation of the status quo.

Ivo Daalder, a former American ambassador to NATO, said that one striking element of the letter was its warning that the U.S. Foreign Assistance Act bars military support from going to any nation that restricts the delivery of humanitarian aid. He said that this reference to U.S. legal obligations would increase its “political impact” in Israel.

The British government added to the pressure, urging Israel to ensure civilians are protected and aid routes remain open. It called an urgent meeting of the U.N. Security Council on Wednesday to discuss the issue.

At the meeting, the U.N.’s acting humanitarian chief, Joyce Msuya, told the Council that it needed to act to address the humanitarian situation in Gaza.

“The level of suffering in Gaza defies our ability to capture it in words, or even to comprehend its scale,” she said. “Reality is brutal in Gaza, and it gets worse every day, as the bombs continue to fall, as fierce fighting continues unabated and as supplies essential for people’s survival and humanitarian assistance are blocked at every turn.”

Aid workers say that extreme hunger in Gaza has been growing for months. The 30-day deadline falls after the U.S. presidential election, potentially making it politically easier for President Biden to take tougher action against Israel than he has so far been willing to.

Matthew Miller, a State Department spokesman, told reporters on Tuesday that aid into Gaza “has fallen by over 50 percent from where it was at its peak” during the war. According to COGAT figures, at least 465 relief trucks entered Gaza over the first half of October, compared to roughly 2,500 over a similar period last month.

On Tuesday, a total of 145 aid trucks entered Gaza through border crossings in the north and south, COGAT said. It added that 610 trucks of aid permitted into Gaza were “waiting for collection” inside the enclave.

Aid groups, for their part, argue that the Israeli military has made it difficult to distribute what little aid is getting into Gaza, often refusing permission for convoys to pass Israeli checkpoints and sometimes firing on them. In addition, Israel’s invasion of the city of Rafah in southern Gaza in May led to the closure of the border crossing there, one of the main conduits for aid.

“The last couple of months, they have not been good at all,” Juliette Touma, a spokeswoman for the main U.N. agency that aids Palestinians, UNRWA, said in an interview on Tuesday.

The letter from the United States also provides a significant show of diplomatic backing for UNRWA at a time when Israel’s Knesset is considering bills that would declare it a terrorist organization. The United States is deeply concerned about the bill and restrictions on UNRWA that would devastate the humanitarian response at a critical moment, the letter said.

A panel of global experts said in June that almost half a million Gazans faced starvation because of a catastrophic lack of food. This has also made it harder for people to recover from illnesses and war-related injuries amid a health care system that has been devastated by the conflict.

“Medical needs are overwhelming,” the medical charity Doctors Without Borders said on Tuesday.

Aaron Boxerman and Farnaz Fassihi contributed reporting.

Israel’s military said that it had been targeting “Hezbollah facilities” in the Dahiya strikes, which took place just after 7 a.m. local time on Wednesday. The attack came about an hour after the Israeli forces had issued an evacuation warning for a building in the area. The human rights group Amnesty International said this week that such warnings were inadequate because they were frequently issued when many people were still asleep and gave little time for residents to take action.

In southern Lebanon, where Israel is engaged in a ground offensive, heavy bombardment in Nabatieh killed at least 16 people and injured more than 50 on Wednesday, according to the Lebanese Health Ministry. The city’s mayor, Dr. Ahmad Kahil, was among the dead, according to Hwaida Turk, the regional governor.

The U.N.’s humanitarian coordinator for Lebanon, Imran Riza, said that the mayor had been part of a relief team that the U.N. had partnered with for more than a year. Four of the team members were killed in the strikes, which occurred just as a crisis meeting was convening in the city’s municipality building, Mr. Riza said.

“Health care facilities, mosques, historical markets, residential complexes and now government buildings are being reduced to rubble,” he said in a statement.

When asked on Wednesday about the strike that killed Dr. Kahil, Matthew Miller, a State Department spokesman, said that if Israel had been “targeting civilians, obviously that would not be acceptable.”

The strikes came a day after Lebanon’s caretaker prime minister, Najib Mikati, said that his government had received “a sort of guarantee” from the Biden administration that Israel would scale back its attacks on Beirut. The White House press secretary, Karine Jean-Pierre, affirmed on Wednesday that the Biden administration had told Israel that it opposed “near-daily strikes” in “densely populated areas of Beirut.”

“We also understand that what they’re conducting — the operations that they’re conducting to destroy Hezbollah infrastructure — is targeted,” Ms. Jean-Pierre said. She added that it was “critical that these operations be conducted in a way” that would not threaten the lives of civilians.

Though Hezbollah exercises de facto control over much of southern Lebanon, including Nabatieh, the group does not enjoy unanimous public support. Dr. Kahil was an elected local government official.

The Israeli military said it had struck “dozens of Hezbollah terrorist targets” in the area, which, it said, included command centers and weapon storage facilities “embedded by Hezbollah adjacent to civilian infrastructure.” The military provided no evidence to support those claims, but Israel has frequently accused Hezbollah of hiding among civilian populations.

At least three more people were killed and 50 others wounded in an overnight strike on Qana, also in southern Lebanon, according to the health ministry. The Israeli military said it had targeted a local Hezbollah commander, along with several other militants. The town was the site of an Israeli strike on a U.N. compound in 1996 that killed at least 100 civilians sheltering there.

Many residents of Nabatieh — once home to tens of thousands — and other cities in southern Lebanon have fled in recent weeks after evacuation orders by the Israeli military. Rema Jamous Imseis, Middle East director for the U.N. refugee agency, said on Tuesday that more than a quarter of Lebanese territory was now under Israeli evacuation orders.

“People are heeding these calls to evacuate,” Ms. Jamous said, “and they’re fleeing with almost nothing.”

Many have taken shelter in school buildings across the country, forcing the facilities to suspend classes, Ted Chaiban, UNICEF’s deputy executive director, told reporters on Wednesday. He said that nearly all public schools were being used as shelters or had been destroyed, and that only 16 percent of the schools were serving students.

Victoria Kim, and Farnaz Fassihi contributed reporting.

The British action follows similar moves taken by its government, the United States and others to address rising Israeli settler violence in the West Bank since the Hamas-led attack in Israel set off a war in Gaza a little over a year ago.

Earlier this month, the U.S. similarly sanctioned individuals and organizations that State Department spokesman Matthew Miller said were “creating an environment where violence and instability thrive.” The U.S. government has taken at least a half dozen similar actions against Israeli settlers and groups supporting or inciting settler violence in the West Bank this year.

Britain in its statement said the measures “follow an unprecedented rise in settler violence in the West Bank over the last year,” noting that the United Nations has recorded more than 1,400 attacks by Israeli settlers against Palestinian communities since last October. The violent encounters often drive Palestinians off their land, the British statement said, allowing Israeli settlers to seize the territory.

The international community largely considers Israeli settlements in the West Bank illegal, and many of the outposts are illegal under Israeli law, too. But they are often tolerated by the Israeli government and sometimes subsequently legalized, granting them formal access to services like running water, electricity, building permits and funding. The far-right government of Prime Minister Benjamin Netanyahu has been expanding settlements.

Palestinians have long argued that the settlements are a creeping annexation enforced by armed settlers and the Israeli military, carving territory that should become a Palestinian state into an unworkable patchwork and steadily pushing Arabs out of their homes and farms.

The recent increase in settler violence has also drawn condemnation from the Israeli authorities. In August, after a riot by Israeli settlers on the Palestinian town of Jit, Mr. Netanyahu’s office issued a statement decrying the attack and pledging to prosecute settlers who acted criminally.

But Mr. Netanyahu’s governing coalition has outspoken supporters of settlements in the West Bank, most notably Finance Minister Bezalel Smotrich and National Security Minister Itamar Ben Gvir. Both vocally oppose the establishment of a Palestinian state, and their proclamations and policies have emboldened some settlers.

This year, Britain, France, Canada, and the U.S. have all imposed sanctions on settlers and organizations that they have said were violating the human rights of Palestinians, destabilizing the West Bank and threatening security for everyone in the area. “The measures taken today are part of wider U.K. efforts to support a more stable West Bank, which is vital for the peace and security of both Palestinians and Israelis,” Britain’s statement said on Tuesday.

Canada and the United States on Tuesday also took action against a group and individual they said were tied to a Palestinian terrorist organization operating in the West Bank and Gaza. In a statement, the Treasury Department said it had designated Samidoun Palestinian Prisoner Solidarity Network, commonly known as Samidoun, as a “sham charity” that raises funds internationally for humanitarian support while actually funding the terrorist organization Popular Front for the Liberation of Palestine, which the U.S. designated as a terrorist organization in 1997.

About 50 patients were able to evacuate daily before the closure, said Adi Lustigman, a lawyer for Physicians for Human Rights Israel, one of the groups that filed the petition. Even that level was just a drop in the bucket, she said, but the medical evacuations trickled to a halt after Israel closed the border crossing. The petition demands that Israel create a transparent process for applications for medical evacuations.

“People don’t know where to turn,” Ms. Lustigman said. Even when people apply for evacuations, there does not appear to be a reasoned approach to when permission is granted, with some critically ill patients still waiting while less sick individuals who applied later are allowed out, she said.

“We didn’t ask Israel to treat people, just to move them in a humane tempo,” Ms. Lustigman said. The petition did not specifically seek that patients be transferred abroad, only that they not be blocked from access to medical care, but Israel prefers for “security reasons” that they travel to a third country, she said.

An unstated reason might be Israeli public opinion, she added. “There is a very strong public objection to the petition as it is,” she said.

Nonetheless, Ms. Lustigman argued, Israel has a responsibility for civilians because it controls Gaza and its borders. “The state is subject to fundamental principles of Israeli law, the principles of administrative law, the Basic Laws, and the rules of natural justice,” Ms. Lustigman noted, and it has obligations under international treaties.

The Supreme Court set urgent hearings about the matter over the summer. Lawyers for Israel expressed agreement on the need for medical evacuations but sought more time in court to show the state was complying. And some permits were granted in the interim. At least 19 sick children, most of them cancer patients, were permitted to leave Gaza for treatment in late June.

But the court’s order on Tuesday puts the focus on the state, the defense minister and the authority responsible for humanitarian coordination in Gaza, known as COGAT, to clarify how the process works. The state has argued at hearings that there is a system, Ms. Lustigman said, but it has yet to convincingly show it.

Israel has until Nov. 11 to provide a response, based on the court’s order. The justice ministry declined to comment on the order. The defense ministry did not respond to a query.

COGAT on Wednesday said in a statement responding to a query about the order that the Israeli military “remains committed to continuing its efforts, in coordination with the international community, to facilitate further exits of patients for continued treatment outside the Gaza Strip, subject to their acceptance by those countries and security screenings.”

The agency noted that the Supreme Court had recognized “that the state is indeed taking actions to allow the exit of patients” but at the same time it “requested the state to explain why it has not published a written procedure on the matter.” COGAT said it was still reviewing the decision.

“Every day that passes with sick and injured individuals in Gaza left without medical treatment means human lives, children and infants are in jeopardy,” Ms. Lustigman and her colleague, Tamir Blank, a lawyer for Physicians for Human Rights Israel who worked on the petition, said in a statement on Tuesday. “The state is obligated to allow access to medical treatment so that those who can still be saved may be saved.”

For many patients, it is already too late. After months of waiting, Fida Ghanem, 42, was granted a permit by Israel and Egypt to leave Gaza for urgent lymphoma treatment in the spring, just before Israeli forces seized the Rafah crossing. With the crossing closed, she died in Gaza in June. The border crossing is still shut.

Aaron Boxerman contributed reporting.

The Israeli military said without elaborating that it had struck a Hezbollah target and that it was examining reports that Lebanese civilians had been killed. “The incident is being examined,” it said in a statement.

The Israeli strike on Monday in the normally sleepy hill village of Aitou, more than 70 miles from the Israeli border, was the first known time since the war began a year ago that the largely Christian region had been hit. The region lies far from Hezbollah’s traditional power bases in southern and eastern Lebanon, and the strike has heightened growing fears that no area in the country is safe.

Rema Jamous Imseis, the U.N. refugee agency’s Middle East director, said on Tuesday that more than a quarter of Lebanese territory had come under Israeli evacuation orders. Nearly a million people in Lebanon have already been displaced, according to the United Nations.

“People are heeding these calls to evacuate,” Ms. Jamous said, “and they’re fleeing with almost nothing.”

Johnatan Reiss contributed reporting.