The last point of refuge for Palestinians fleeing from Israel’s relentless siege of Gaza is collapsing under the weight of tens of thousands of people seeking food and shelter, stirring fears of a potential mass displacement into Egypt, United Nations officials warned on Sunday.

Pressure is mounting in the area near Gaza’s southern border with Egypt, Rafah, where many Palestinians have tried to escape Israel’s military campaign against Hamas, only to find more death, hunger and desperation.

“Where should I go? Tell me, where should I go?” said Raif Naji Abu Lubda, 39, a farmer who fled to the border area with his wife and six children.

The family is now sleeping on the ground in the cold and cannot find food or even salty water to drink, he said.

Still, Mr. Abu Lubda said, he would rather “go home and die there” than be forced into Egypt’s Sinai Peninsula — a scenario that Egypt and other Arab governments in any event have flatly rejected, fearing that if large numbers of Palestinians leave Gaza, Israel won’t allow them to return.

In some wars, civilians can escape the violence by fleeing to neighboring countries, with the understanding that they will return home after the fighting stops. But the displacement of Palestinians caused by the creation of Israel in 1948 and the decades of conflict since has left Arab governments scared that Israel might use the war to push Palestinians from Gaza permanently.

Speaking at a conference in Qatar on Sunday, Jordan’s foreign minister, Ayman Safadi, said that Israel’s military campaign amounted to “a systematic effort to empty Gaza of its people.” Much of Jordan’s population are Palestinians whose ancestors fled or were driven from what is now Israel — an event that Palestinians call the “Nakba,” or catastrophe, and consider a deep historic trauma.

At the same conference in Qatar, the United Nations secretary-general, António Guterres, raised concerns that the terrible conditions for Palestinians crowded near Gaza’s border with Egypt created the possibility of a “mass displacement” into the Sinai.

“There is no effective protection of civilians in Gaza,” Mr. Guterres said. “I expect public order to completely break down soon, and an even worse situation could unfold.”

An Israeli government spokesman, Eylon Levy, called the Jordanian foreign minister’s allegations “outrageous and false.”

“Israel is fighting to defend itself from the monsters who perpetrated the Oct. 7 massacre, and the purpose of our campaign is to bring those monsters to justice and ensure they can never again hurt our people,” he said at a news conference.

Gaza’s border crossing with Egypt became critical after Israel imposed a siege on the territory in response to the attack carried out by Hamas, which runs Gaza. Hamas forces killed some 1,200 people, according to the Israeli authorities. The Israeli military assault that followed has killed more than 15,000 people in Gaza, according to health authorities there — a bombing campaign whose intensity has few precedents this century.

With Israel largely shuttering its crossings with Gaza, Rafah has become the entry point for the vast majority of aid, and an exit route for a small number of people.

With Israeli forces attacking southern Gaza, Gazans have flocked to the border area in search of safety and supplies. Thousands are arriving daily, following Israeli evacuation orders that described the area as safe.

But relief is in short supply. Aid workers have warned of “extreme” overcrowding and a “dire” situation. Those deteriorating conditions, officials fear, could push Palestinians over the border into Egypt.

Philippe Lazzarini, the commissioner general of the United Nations Relief and Works Agency, which takes care of Palestinian refugees, said that even if there was no “deliberate policy” to do so, Israel’s military operations were “putting more and more pressure for this type of scenario to unfold.”

“The population has been pushed more and more into tinier and tinier and tinier pieces of land in the Gaza Strip, and there is no way that this piece of land will be able to accommodate such a high number of people,” he said in an interview on Sunday.

Gazans who have fled to the area thinking that the south would be safe have found that Israel is bombing there, too.

“We have no other place — and no safe place,” said Ziad Obeid, a Palestinian civil servant.

Mr. Obeid and his family ended up on the outskirts of Rafah after fleeing farther and farther south during the war.

“We are fighting day and night just to get some bread, water and vegetables,” he said, recounting failed attempts to find eggs for his elderly mother.

The Israeli government has not publicly called for large numbers of Gazans to move to Egypt. But diplomats have said that in private, Israel has pushed for them to be housed there for the duration of the war.

Egyptian leaders adamantly oppose the idea, partly out of economic and security concerns, and partly out of concerns that it would destroy hopes to include Gaza in a future Palestinian state.

Gazans must “stay steadfast and remain on their land,” President Abdel Fattah el-Sisi of Egypt said in October.

Egypt’s army has erected sand barriers and stationed tanks and other military vehicles along the border at Rafah, according to two people who live near the border and spoke on the condition of anonymity because of the sensitivity of the issue.

In 2008, Hamas broke down parts of the border fence, allowing tens of thousands of Palestinians to stream into northern Egypt. That temporarily broke the blockade that Egypt and Israel had imposed on the territory after Hamas took it over the year before. Palestinians returned with medicine, cement, sheep, gasoline, soap and other supplies that had become rare in the strip.

At the time, Israeli officials said that — if controlled — the border opening to Egypt might allow Israel to lock the door to a Hamas-run Gaza and let Egypt deal with the poverty and problems there.

Today, many Palestinians fear that Israel’s plan since the war began has been to make conditions in Gaza so dangerous and miserable that Gazans are forced to flee into Egypt.

“The developments we are witnessing point to attempts to move Palestinians into Egypt, regardless of whether they stay there or are resettled elsewhere,” Mr. Lazzarini wrote in an opinion article this week in The Los Angeles Times.

The internal displacement of millions of Gazans to the southern part of their territory was “the first stage of such a scenario,” he argued. “The next stage is underway — forcing people out of the urban center in Khan Younis and closer to the Egyptian border,” he wrote.

United Nations facilities that have been turned into shelters are completely overwhelmed, and many Gazans are living in the streets or in makeshift shelters, with no sanitation and not enough food, Mr. Lazzarini said in the interview on Sunday.

“We are punished for something that we don’t have any role in,” said Mr. Obeid, the Palestinian civil servant. “The civilians who are being killed day and night all around Gaza should not be punished.”

Mr. Abu Lubda, the farmer, lamented that Gazans felt abandoned by the world.

“The United Nations doesn’t care about us, the Security Council doesn’t care about us, the Arab League doesn’t care about us, no one cares about us,” he said. “They threw us in the streets.”

Patrick Kingsley contributed reporting from Jerusalem, and Nada Hussein and Vivian Yee from Cairo.