Israel said that the Kerem Shalom crossing reopened on Wednesday, but did not indicate when the Rafah crossing would reopen. The U.N. disputed Israel’s claim.

The fighting in the Rafah area and the closure of the crossings set aid efforts back, at least temporarily, to the conditions of the first weeks of the war, when an Israeli and Egyptian blockade prevented anything from entering Gaza, producing desperate shortages of food, water, fuel, medicine and other supplies. Israel has described the military action it began on Monday as a limited incursion into Rafah that seized control of the border crossing, not the full-fledged offensive it has vowed to carry out, despite warnings from the United States and aid groups that it would be a humanitarian catastrophe.

U.N. officials said the conditions threaten to halt all its humanitarian operations in Gaza.

As many as a million people displaced from other parts of Gaza, more than half of them children, have sought refuge there, living in squalid conditions and relying on international aid efforts.

“Rafah is the epicenter of humanitarian operations in Gaza,” António Guterres, the U.N. secretary general, said on Tuesday. “Attacking Rafah will further upend our efforts to support people in dire humanitarian straits as famine looms.”

Before the war began last October, about 500 aid trucks and additional commercial trucks a day carried supplies into Gaza, home to some 2.3 million people. Even after deliveries resumed, they were a fraction of the prewar level, as Israel kept most crossings closed, insisted on close inspection of every load, and barred some supplies.

After intense international pressure on Israel, including from the United States, the average rose to more than 200 humanitarian aid trucks a day in second half of April and the first days of May, according to the United Nations, still well below what aid agencies said was needed and what the Biden administration had called for. No commercial trucks have entered Gaza since the war started in October.

For months the United Nations and aid groups have also struggled to gain access and safe passage for their staff to work in Gaza, despite intense negotiations with Israel.

Now, U.N. officials say that the limited progress they had made is in jeopardy.

“We are managing the whole aid operation opportunistically as opposed to holistically — if there is something we can grab we will grab it,” said Stéphane Dujarric, the U.N. spokesman, in an interview on Wednesday.

“We want the ability to work without being in the middle of a conflict zone and people we are trying to help being terrified,” he added.

A day earlier the leader of the U.N.’s humanitarian office for the Palestinian territories, Andrea De Domenico, said from Jerusalem in a video briefing with reporters that fuel would run out in days, cutting off communications, shuttering hospitals and halting distribution of food and other essential aid.

Gaza’s electrical grid stopped working early in the war. The only power available now comes from generators, making fuel essential.

The presence of Israeli tanks and fighting around Rafah’s border had made it impossible for the U.N. to access fuel in storage facilities in the area, Mr. De Domenico said. He added that people are fleeing Rafah to areas where there was no shelter, clean water and drainage.

“It is impossible to improve the situation existing in the new displacement sites without the entry of supplies and without the fuel to transport them to the location where the people are concentrating,” said Mr. De Domenico.

If the area around the Rafah crossing becomes a battle zone, U.N. officials said, it would be nearly impossible to deliver and distribute the aid.