Others have chosen to head south despite the risks. The Israeli military, having cut off northern Gaza from the south, said it was offering four-hour windows for residents to head south safely in recent days.

About 5,000 people used that lull to make the trip on Monday through areas held by Israeli troops, United Nations monitors said. They trudged south on foot, carrying their small children and belongings.

On Tuesday, an Israeli military spokesman posted footage on X of a caravan of Gazans heading south on foot and waving white flags. The Israeli military has also claimed that Hamas has been physically hindering people’s movement to the south, which Hamas has denied.

Others have left the north only to come back. Bushra Khalidi, Oxfam International’s policy lead for the Palestinian territories, said that her in-laws were among the many people who had abandoned their homes in Gaza City, only to return. In their case, the place where they had sought refuge, in central Gaza, received an evacuation order from the Israeli military.

“My father-in-law said ‘I’d rather die with dignity in my own home than die in a stranger’s house,’” she said.

Their neighborhood, Rimal, once an elegant part of the city, has been pummeled by airstrikes. They are alternating between nights at home and camping out near Al Shifa Hospital, along with tens of thousands of other displaced people, Ms. Khalidi said.

Many Palestinians had hoped the hospital and the adjacent area would be spared, but there have been Israeli strikes there, too, including one on Friday that the hospital chief, Dr. Mohammad Abu Salmiya, said killed 13 people. The top floor of one hospital building was hit on Monday, killing a child and wounding 10 others, he said.

Israel has charged that Hamas is operating a command center underneath Al Shifa, which is the territory’s largest hospital; Hamas denies that.

“We won’t leave the hospital no matter what happens,” Dr. Abu Salmiya said.

Israel has besieged Gaza since the Oct. 7 Hamas-led attacks in Israel, allowing only limited deliveries of food, water and medical supplies through the Rafah crossing — far less than humanitarian groups say is needed.

Conditions are worst in the north, where almost no aid has been delivered. And Israel has not allowed any fuel into Gaza, despite its importance to operating water and hospital equipment, the territory’s only power plant, delivery trucks, ambulances and generators.

Ms. Khalidi stressed that without a cease-fire, there was no way to safely deliver aid anywhere in the territory.

“How are humanitarian workers supposed to deliver aid when there’s bombings, the roads are damaged and we have direct evidence of indiscriminate attacks?” she said.

Arijeta Lajka, Riley Mellen, and Iyad Abuheweila contributed reporting.

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