Just a few weeks ago, Israel, under extraordinary international pressure to respond to warnings of imminent famine in the Gaza Strip, announced new steps to increase humanitarian aid.

But after an Israeli military incursion into the southern city of Rafah this week, the flow of aid has come to a near-total stop, first closed off by Israel and then further restricted, officials say, by Egypt.

Aid officials warned that essentials such as food and medicine were running dangerously low, threatening to worsen an already dire humanitarian crisis.

“I’ve never been involved in a situation as devastating, complex or erratic as this,” Hamish Young, senior emergency coordinator in Gaza for UNICEF, the children’s agency, said Friday.

Although Israel said it allowed 200,000 liters of fuel into southern Gaza on Friday, that may offer only a temporary respite for hospitals and bakeries, which rely on generators for electricity, United Nations officials said.

Most of the aid for Gaza had been entering through two border crossings in the southern end of the territory.

Israel shut down one of those crossings, Kerem Shalom, after a Hamas rocket attack nearby killed four Israeli soldiers Sunday. The next day, Israeli forces seized and closed the second crossing, in Rafah, on the Egyptian border, and raised the Israeli flag there as part of what the military described as a limited operation against Hamas.

Although Israel has since reopened Kerem Shalom and some fuel has gone into Gaza from there, no other vital supplies such as food and medicines have been allowed through the crossing since Sunday, according to Scott Anderson, a senior official at UNRWA, the main U.N. agency that aids Gaza.

One reason is that Egypt, where most of the aid for Gaza is collected and loaded, is refusing to allow trucks from the closed 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 U.S. and Israeli officials say they believe that Egypt is trying to pressure Israel to pull back its forces from Rafah.

Another official familiar with the negotiations said U.S. officials — including William Burns, the CIA director, who was in Cairo this week for cease-fire talks — had been trying to persuade Egypt to dispatch the trucks. But Egypt has rebuffed the pressure, saying it will not allow aid to flow to Kerem Shalom while Israel has closed the Rafah crossing and casting the situation as a matter of national sovereignty, a U.N. official said.

All the officials spoke on condition of anonymity because negotiations were still underway. A spokesperson for Egypt’s government declined to comment.

Israel has threatened a full-scale invasion of Rafah, saying its security depends on the elimination of Hamas battalions hiding there. But it is facing intense pressure from its closest ally, the United States, to scale back its war aims in the city, where about 1 million Palestinians are sheltering. This week, U.S. officials disclosed that President Joe Biden had withheld thousands of heavy bombs for Israel out of concern that they could be dropped on densely populated areas of Rafah.

Egypt, too, has grown increasingly nervous about Israel’s Rafah operation, in part over deep-seated fears that it will push Palestinian refugees onto Egyptian soil — an outcome Egypt views as a national security threat. Israel’s presence on the Egyptian-Gaza border, which Egypt previously controlled, has also drawn heavy domestic criticism.

Egyptian concerns are not the only factor complicating the use of Kerem Shalom. The Western official said Israeli military activity and fighting near the crossing had damaged roads, making it extremely difficult for aid trucks to enter Gaza.

The area is also considered unsafe for aid workers, according to one of the U.S. officials and the U.N. official, who said Israeli forces shot at a U.N. contractor near Kerem Shalom on Wednesday.

An Israeli military spokesperson, Maj. Nir Dinar, declined to comment on the episode, but he blamed Hamas for preventing aid from entering. He said the Kerem Shalon crossing had been closed only after Hamas fired on the area three times this week.

“Israel is doing everything to enable” aid to enter, Dinar said.

Although aid deliveries rose in April and the first days of May, before the Rafah operation, aid groups said Israel was not allowing nearly enough into Gaza to stave off famine or the collapse of the health care and sanitation systems. Now that tens of thousands more civilians are fleeing Rafah to areas with little infrastructure set up to care for them, the United Nations and aid groups say the situation has become far more dire.

On Friday, UNRWA reported that about 110,000 people had fled Rafah this week amid intensifying Israeli airstrikes and growing fears that a major military invasion was imminent.

One of those who fled was Saeda al-Nemnem, 42, who had given birth to twins less than a month ago. Members of her family, which was displaced from Gaza City, sent a relative to look for a truck that could take them north.

But the relative, Mohammed al-Jojo, never made it back. He was killed by an Israeli strike on the tractor he was riding, al-Nemnem said. He “was killed when he was getting us out of that area to a safer place,” she said. “I feel I caused his death.”

Despite the dangers on the road, she and her family of eight traveled to the southern city of Khan Younis, where they found shelter in a room attached to Al-Aqsa University’s main building. There, they could hear what seemed like explosions from Israeli bombs, missiles and artillery, she said.

“My children’s heartbeats were so high that I could feel them,” she said. It was the heaviest bombardment she had ever heard, she said, “so close and so terrifying for me and my children.”

Manal al-Wakeel, 48, who had helped the aid group World Central Kitchen prepare hot meals, said she and her family had been sheltering in a part of Rafah that was battered by Israeli airstrikes and ground combat.

On Tuesday night, al-Wakeel said she, her husband, their 11 children and other relatives found a truck that would take them and their belongings, including suitcases of clothes, pots, pans and tents, for 2,500 shekels (about $670) in search of another place to stay.

They left Rafah around midnight and made their way north, along with hundreds of tuk-tuks, trucks, cars and donkey carts full of other displaced families and their possessions.

“It was a scary night; the truck was moving slowly because of the heavy load on it,” she said.

Once out of Rafah, they stopped at schools and other buildings, looking for places to stay. But they were all full.

Others couldn’t find shelter, either, and al-Wakeel said she saw many people sleeping by the side of the road, next to the few belongings they had fled with.

At a U.N. school in Deir al Balah, a young man suggested they stay in an empty, windowless concrete building that belonged to the Hamas-led government’s ministry of social development.

“It looked like a dangerous place,” she said, adding that they had been told that a woman and her daughter had been killed by an Israeli missile there.

But they were too afraid to continue traveling in the darkness, and decided to spend the night there and to look for a safer place in the morning.

“I feel so sad and disappointed for what happened to Rafah, as it was stable for us there,” she said. “We have spent so much time having to arrange new places for ourselves again and we feel depressed and so exhausted from repeating the same suffering.”

The New York Times New Service