Israel pushes into south Gaza. A school is bombed, a hospital, overwhelmed.

The bodies of around 20 people killed in a strike, wrapped in white sheets, lay in the yard outside the hospital morgue Tuesday morning. Relatives shouted and wept.

Israel has vowed to destroy Hamas. Yet the group remains largely intact.

The Israel Defense Forces on Tuesday pushed into Khan Younis, expanding their war against Hamas on a new front and bringing fresh horror to Palestinians who say they now have nowhere to run. Until now, southern Gaza’s largest city had been a haven for civilians fleeing Gaza City and the north.

More than 80 percent of Gaza’s population of more than 2 million has been displaced, according to the United Nations. Many have gathered in schools and hospitals in the south in the expectation that they would be spared. The school in the Maan neighborhood of Khan Younis was bombed early Tuesday.

Hamad Abu Sarhan, 51, and his family had sought shelter there after Israeli forces ordered civilians to evacuate other areas in the south. They had been there for two days when it was attacked. Abu Sarhan’s 28-year-old nephew was killed.

“The situation is truly catastrophic,” Abu Sarhan said.

Hostages freed by Hamas and angry relatives of those still held in Gaza told Israel’s security cabinet Tuesday that they feared the fighting would endanger those who remain in Gaza.

“What I see on TV scares me a lot,” one former hostage said, according to Haaretz. “I see [Israeli] bombings there, and you have no idea where the captives are. … I was in a house surrounded by explosions. We slept in tunnels, and we feared not Hamas, but Israel might kill us, and then it would have been said, ‘Hamas killed you.’”

Khan Younis is home to Yehiya Sinwar, the Hamas military chief in Gaza and the top target on Israel’s list. It had a population of around 400,000 before the war, but the count ballooned as Israel focused on the fighting in the north.

Fighting continues to rage in the north. As more people are displaced, the United Nations says it is running out of tents to give to the displaced.

The current hostilities began Oct. 7, when Hamas and allied fighters overran communities in southern Israel, killing more than 1,200 people and taking more than 200 hostages. Israel’s goal now is to destroy Hamas as a military and political force.

Israel said Tuesday it was intensifying its efforts. In addition to moving into Khan Younis, Israeli forces entered the dense Gaza City neighborhoods of Jabalya and Shejaiya, where Hamas is thought to be deeply dug in.

Israel has said repeatedly that it is abiding by international law and seeking to minimize civilian casualties, but aid agencies say conditions for civilians are dire.

“The situation is getting worse by the hour,” Richard Peeperkorn, the World Health Organization’s representative in Gaza, told reporters Tuesday. “There’s intensified bombing going on all around, including here in the southern areas, Khan Younis and even in Rafah” on the enclave’s border with Egypt.

Abu Sarhan said the bombing overnight was intense. “It was the hardest night of my life,” he said. “We were surrounded by belts of fire from everywhere. The attacks by planes and tanks did not stop throughout the hours of the night.”

Injured in the attack were Abu Sarhan’s brother, his 15-year-old niece and his 7-year-old nephew. Ambulances could not reach the area, he said; the injured were taken out in private vehicles. Buses came later to transport survivors.

“When we left the place, there were corpses everywhere and in the streets,” he said. “There were screams from people trapped in their homes.”

Ibrahim Abu Awwad was injured in the strikes. “People were sprawled on the ground, some with severed limbs,” he said.

Israel has said it is has started a new phase in its campaign: urban fighting. “We’re moving ahead with the second stage now,” government spokesman Eylon Levy said, “a second stage that is going to be difficult militarily.”

“We are talking about close-quarter fighting that engages terrorists emerging from tunnels and buildings,” Levy said.

Fighting in Gaza resumed Friday after a seven-day break to allow the exchange of hostages and the entry of more humanitarian aid. Each side accused the other of breaching the truce.

“Those who thought that the IDF would not know how to renew the fighting after the pause were mistaken,” Chief of the General Staff Herzi Halevi said. “Hamas is already feeling this.”

Tamim bin Hamad Al Thani, the emir of Qatar, called on the U.N. Security Council to force Israel to return to negotiations to end the war. He called it “shameful” that the international community was not doing more to stop the bloodletting.

Gaza’s health-care system continues to collapse. Palestinians sheltering at Kamal Adwan Hospital in Beit Lahia on the northern edge of Gaza said they were surrounded by Israeli tanks and unable to leave. “Anyone who tries to go out gets shot,” Anas Sharief, a journalist with Al Jazeera, said in a video message. “We ask God for safety.” Kamal Adwan, northern Gaza’s only remaining government hospital, was out of service Tuesday, according to the Gaza Health Ministry.

More than 400,000 people in northern Gaza are completely without medical services, the ministry said.

With much of the staff of al-Nasser Hospital in Khan Younis unable to reach the facility, emergency department head Mohamed Qandeel said that he and three other doctors had treated 80 severely injured patients. Twenty of the injured needed surgery, and 10 needed intensive care, he said. “These days we cannot forget,” he said. “They are catastrophic days.”

Harb reported from London, Morris from Jerusalem, Balousha from Amman, Jordan, and Mellen from Washington. Miriam Berger in Jerusalem and Cate Brown in Washington contributed to this report.