Six trucks of flour arrived through the Kerem Shalom crossing on Saturday, and on Friday, some fuel also came through the same crossing point, according to Juliette Touma, the communications director for the main U.N. agency that aids Palestinians, UNRWA. She said that no other supplies arrived through Kerem Shalom this past week and that the Rafah crossing remained closed.

“That’s all since May 6,” Ms. Touma said in a text message. “Basically nothing.”

The Israeli agency that coordinates aid to Palestinians, COGAT, said on Sunday that Israel was “operating to enable the flow of aid to Rafah” through a road that runs through part of the length of the enclave. It did not provide additional details.

The extremely limited amount of aid will almost certainly aggravate a cumulative food deficit that has built up in the past seven months.

Before the war began last October, about 500 aid trucks and additional commercial trucks a day carried supplies into Gaza. But the number entering the territory through the two main border crossings has fallen by about 75 percent since Oct. 7, according to the United Nations. Some food has also been delivered by air and sea and, more recently, through the Erez border crossing in northern Gaza, but aid groups say it is insufficient to make up for the deficit at the main border crossings.

At the same time, Ms. Touma said that around 300,000 liters of fuel is needed per day for all humanitarian purposes, including to run generators in hospitals and relief operations. Aid groups said last week that they had just a few days of fuel stocks left.

Only 157,000 liters of fuel entered Gaza on Friday, Ms. Touma said. COGAT put the figure at 200,000 liters. The reason for the discrepancy was not immediately clear.

“At this desperate moment, exacerbated by acts impeding the entry of humanitarian aid in Gaza through the three crossings, there is a dire shortage of fuel, which is hindering everything,” Volker Türk, the U.N.’s high commissioner for human rights, said in a statement on Sunday.

Israel’s military said that Hamas’s deadly rocket attack toward Kerem Shalom last Sunday was launched from the area of Rafah, in southern Gaza. When Israel’s military captured the Rafah border crossing last week, it told people to evacuate from the east of the city. Since then, the military has expanded the evacuation orders.

Mr. Türk said that he could “see no way” that the latest evacuation order imposed on civilians in Rafah “can be reconciled with the binding requirements of international humanitarian law.”

In Nuseirat, in central Gaza, the local authorities were bracing for a potential public health crisis, the town’s mayor, Iyad Maghari, said in a statement released on Sunday by Gaza’s government press office.

Mr. Maghari said the municipality had only 48 hours worth of fuel left and would soon have to halt what few services remained after seven months of war.

“We call on all U.N. organizations to intervene urgently and quickly to supply the fuel necessary to operate water wells, sewage pumps and waste collection,” Mr. Maghari said in the statement, adding that otherwise Nuseirat could soon see “sewage overflowing and waste piling up in the streets.”

One reason for the overall hold up in aid is that Egypt, where most of the assistance for Gaza is collected and loaded, is refusing to allow trucks from the Rafah crossing to drive on to Kerem Shalom, according to two U.S. officials and a Western official who are involved in the aid operation, as well as two Israeli officials with knowledge of the situation. The American and Israeli officials say they believe Egypt is trying to pressure Israel to pull back its forces from Rafah.

After rocket sirens sounded in the area of Kerem Shalom again on Sunday, Israel’s military said that two launches from Rafah had been intercepted by air defenses.

Liam Stack contributed reporting.