One official said that negotiators did not believe that Hamas or Israel were leaving the negotiations permanently. And a senior Egyptian official told state-owned television that mediation efforts were still underway to bridge the differences between Israel and Hamas.

Hamas is seeking an end to the war and the complete withdrawal of Israeli troops, while Israel is offering a temporary cease-fire. Mr. Netanyahu has said that Israel will not stop fighting until Hamas is eliminated and all the hostages are freed.

Israel’s incursion into Rafah this week has displaced about 80,000 people there, most of whom are now sheltering in the southern city of Khan Younis or along the Mediterranean coast in Deir al Balah, both areas that lack basic services, Farhan Haq, a United Nations spokesman, said on Thursday.

The Israeli military had told about 110,000 civilians to evacuate parts of Rafah, which has become a refuge for hundreds of thousands of displaced Palestinians, many of them living in tents without adequate food, water and sanitation.

Riyad al-Masry, a sign language interpreter, said on Thursday that he and his extended family had left Rafah even though he had already moved five times since the war began. The prospect of a sixth move was “torture beyond torture,” he said — but he said nearby fighting gave him little choice.

“We are almost in the middle of danger,” Mr. al-Masry said.

Mr. Haq said that goods and fuel had not entered through the Rafah crossing in recent days and that hospitals may have to shut down their generators in a few days. He said the World Food Program had reported that its main warehouse in Gaza was inaccessible because of fighting and that only one bakery in Gaza was still operating.

Jens Laerke, a spokesman for the U.N. humanitarian office in Geneva, described Rafah as a “highly active war zone,” and said it presented “serious challenges” for aid distribution in southern Gaza and farther north in the territory.

“We reiterate that the parties’ obligation to facilitate aid does not end at the border or in a drop-off zone,” he said. “Aid must safely reach those who need it.”

Reporting was contributed by Matthew Mpoke Bigg, Iyad Abuheweila, Myra Noveck, Aaron Boxerman, Vivian Yee, Erica L. Green and Farnaz Fassihi.