The pressure on Egypt is building.

More than half of Gaza’s population is squeezed into miserable tent cities in Rafah, a small city along Egypt’s border, left with nowhere else to go by Israel’s military campaign.

Prime Minister Benjamin Netanyahu of Israel has threatened to overrun the area, and on Friday, he directed his forces to plan the evacuation of civilians from Rafah to clear the way for a new offensive against Hamas.

But it is not clear where those people could go.

Rather than opening its border to give Palestinians a refuge from the onslaught, as it has done for people fleeing other conflicts in the region, Egypt has reinforced its frontier with Gaza. It has also warned Israel that any move that would send Gazans spilling into its territory could jeopardize the decades-old Israel-Egypt peace treaty, an anchor of Middle East stability since 1979.

Israel’s next steps in the war could force such a breaking point.

During past conflicts in the region, Egypt has taken in refugees from Syria, Yemen and neighboring Sudan. But in this war, it has reacted very differently to the plight of its Arab neighbors, spurred by a mix of alarm over its own security and fear that the displacement could become permanent and undermine Palestinian aspirations for statehood.

Egyptian leaders are also wary of the Islamist Hamas stoking militancy and spreading influence in their country, as Egypt has spent years trying to quash Islamists and an insurgency at home.

A Hamas-led attack on Israel on Oct. 7 set off the war in Gaza, and Mr. Netanyahu has called Rafah one of “Hamas’s last remaining strongholds.” However accurate that label, Rafah is also now the full-to-bursting shelter of last resort for about 1.4 million hungry, desperate people, according to the United Nations, most of them displaced from elsewhere in Gaza.

Egyptian officials have urged their Western counterparts to tell Israel that they see any move to force Gazans to cross into Sinai as a violation that would effectively suspend the 1979 peace treaty, according to a senior Western diplomat in Cairo. Another senior Western official, a U.S. official and an Israeli official said the message was even more direct, with Egypt threatening to suspend the treaty if the Israeli military pushed Gazans into Egypt.

The Egyptian government repeated that warning to Secretary of State Antony J. Blinken on Wednesday, when Mr. Blinken was in Cairo to meet with President Abdel Fattah el-Sisi, the Israeli official said.

The U.S. official said Egypt had made clear it was prepared to militarize its border, perhaps with tanks, if Palestinians begin to be pushed into Sinai.

While Egyptians have never warmed to Israel in more than four decades of peace, their treaty has been one of the few stable constants in a turbulent region. Egypt has benefited from the security cooperation and from the generous American support — including more than $1 billion in annual aid — that it brought.

And despite the rising tensions, Egyptian and Israeli officials are still communicating with each other.

The Israeli official said that military officers from both countries, who have a long-established relationship of trust born of security cooperation around the border, are also speaking privately about Israel’s likely incursion into Rafah. In those discussions, the Egyptians asked Israel to limit the operation’s scale, this official said.

The two countries, which have jointly enforced a crippling blockade on Gaza since Hamas took control in 2007, are also discussing giving Israel a greater role in securing the narrow buffer zone that runs along the approximately nine-mile border between Egypt and Gaza, according to regional and Western officials.

But state-owned Egyptian media outlets have published anonymous denials by Egyptian officials about any agreement, signaling the Cairo government’s reluctance for its population to see any hint of cooperation with Israel. And Israel’s talk of controlling the zone has only added to strains in the relationship.

Egypt is Gaza’s only neighbor other than Israel, and since Israel invaded the territory in October, Egypt has helped about 1,700 gravely wounded Palestinians leave Gaza for treatment in Egyptian hospitals.

But Cairo categorically rejects any larger influx of Palestinian refugees onto Egyptian soil.

“There is a difference between hosting refugees and agreeing on forced displacement of a people,” Hani Labib, a pro-government commentator in Egypt, said Tuesday on an evening talk show.

The sensitivity dates back to 1948, when hundreds of thousands of Palestinians fled or were expelled from their homes in the war surrounding Israel’s creation, never to return.

Many Palestinians and other Arabs refer to this chapter in history as the nakba, Arabic for catastrophe, and the permanent displacements of 1948 have reverberated in the Arab world’s memory as an injustice never remedied.

To many people in Egypt and across the Middle East, Israel forcing Gazans to leave their homes during this war, and perhaps flee Gaza altogether, would amount to a second nakba.

Early in the war, Israel pushed in diplomatic discussions for Gazans to move to Sinai, but Israeli officials have stopped formally advocating this since November.

Still, comments by hard-line Israeli government ministers endorsing the expulsion of Palestinians from Gaza and open calls from some Israelis to rebuild Jewish settlements in the enclave have fed Arab fears that, after the war, Gazans who leave would be unable to return — further undermining hopes for a future Palestinian state.

Those worries also set Gazans apart from refugees in other crises.

Though some Gazans have said in interviews with The Times that they hope to escape to Egypt as the war has intensified, many, motivated by a bone-deep commitment to the dream of statehood, reject any suggestion of abandoning their homeland.

“Egypt is not an option for me to run to,” said Fathi Abu Snema, 45, who has been sheltering in a Rafah school for four months. “I prefer to die here.”

Egypt’s president, Mr. el-Sisi, has sworn repeatedly to reject what he calls the “liquidation of the Palestinian cause,” winning applause even from Egyptians frustrated with him on other grounds.

But perhaps more important, Cairo also dreads what Palestinian refugees in Sinai would mean for Egypt’s security. Restive, embittered refugees could launch attacks at Israel from Egyptian soil, inviting Israeli retaliation, or be recruited into the local insurgency in Sinai that Egypt has battled for years.

Egypt also fears the spread onto its territory of Hamas because of its origins as an offshoot of the Muslim Brotherhood, the Egyptian Islamist political organization. The Brotherhood came to power in free elections after Egypt’s 2011 Arab Spring uprising. But Mr. el-Sisi’s regime, which overthrew the Brotherhood in 2013, has vilified the group as terrorists and spent the past decade trying to eradicate it from Egypt.

In another sign of the growing pressure on Egypt, Israel wants control over the narrow buffer zone separating Gaza and Egypt’s Sinai Peninsula.

Mr. Netanyahu has said that Israel must control the zone, known as the Philadelphi Corridor, and analysts say Egypt is worried that Israel wants to seize it as a means to push Gazans into Sinai.

Israeli leaders have cited security concerns, saying Hamas smuggles weaponry through the Gaza-Egypt border zone.

But years ago, Egypt destroyed the main smuggling tunnels from its territory into Gaza, flooded them with seawater and razed the buildings that provided cover for people using the tunnels. It argues that it has done its part to sever smuggling routes.

Israeli military and intelligence officials have concluded that a significant amount of Hamas’s weaponry comes not from smuggling, but from unexploded munitions fired by Israel into Gaza and recycled by Hamas, as well as from arms stolen from Israeli bases, according to a recent Times investigation.

Sinai is such a sensitive region for Egypt that it normally bars most nonresidents from entering it, including journalists. But interviews and videos taken in recent years by the Sinai Foundation for Human Rights, a Britain-based group that monitors abuses in the area, show that the Egyptian military continued working to destroy new tunnels until at least late 2020. The material was shared with The Times.

The group interviewed five smugglers in Sinai who said smuggling between Egypt and Gaza came to a halt at least two years ago. It also spoke to an Egyptian soldier stationed at the border who said troops were ordered to shoot any moving object they spotted in the area to deter smuggling. Its staff has observed the Egyptian military using patrols, drones and bulldozers to guard against smuggling.

With its military outmatched by Israel’s and its economy mired in a deep crisis, Egypt has few options for bending Israel to its will. And its mountain of debt and desperation for foreign currency have raised questions over whether Israel’s Western allies could offer rich enough financial incentives to persuade Egypt to resettle Gazans in Sinai.

But so far, Western leaders, fearing instability in Egypt, have instead pressed Israel to refrain from displacing Gazans to Egypt.

Reporting was contributed by Patrick Kingsley, Zolan Kanno-Youngs and Adam Rasgon from Jerusalem, Nada Rashwan from Cairo, and Abu Bakr Bashir from London.