For Israel, too, more than four decades of a so-called “cold peace” with Egypt has proved to be an essential pillar of national security. The alliance gave Israel a path to better relations with its Muslim neighbors, paving the way for its normalization of ties with more countries and making it an increasingly integral part of a regional, anti-Iranian axis.

Still, Israel took the risk of upsetting the delicate balance because it says it needed to take control of the Philadelphi Corridor to destroy dozens of tunnels under the border that it says have enabled Hamas to smuggle arms into the strip — despite Egypt’s avowals that it put a stop to the smuggling years ago.

The Israeli military’s push into southern Gaza and the city of Rafah in recent weeks has now put a serious strain on ties between the two countries, raising questions about how far Israel will go in insisting on complete control over the border area, and how much of a continued Israeli presence there Egypt can tolerate.

Egypt’s patience with Israel’s military moves is wearing dangerously thin, as it has repeatedly made clear. Not only is the government panicked at the prospect of Gazans fleeing the Rafah fighting over the border into Egypt, but it is also determined to show its public that it is standing up to Israel, which most Egyptians still regard as an enemy despite the 45-year-old peace treaty.

Cairo has registered to speak in support of South Africa’s case at the International Court of Justice accusing Israel of committing genocide in Gaza. And it has warned that Israel is jeopardizing the 1979 peace treaty between the two countries, which grew out of what are known as the Camp David Accords.

Though it has denounced Israel for cutting off humanitarian aid to Gaza, Egypt itself temporarily stopped the flow of aid trucks from its own territory, where most aid accumulates before being trucked to the Palestinian strip — an attempt to pressure Israel into withdrawing from the Rafah crossing. That border point, the main conduit for aid and other supplies during the war, lies between Egypt and Gaza but was recently occupied by Israel, drawing public outrage in Egypt.

Egypt has refrained from taking more serious steps to respond to Israel’s moves, such as withdrawing its ambassador from Tel Aviv. And the government-managed news media appears to have been helping with efforts to limit public outrage.

Egypt is “ready for all scenarios, and will never allow any encroachment on its sovereignty and its national security, either directly or indirectly,” Ahmed Moussa, a prominent talk-show host, wrote in a column for Al-Ahram, Egypt’s flagship daily newspaper, on May 17.

Yet when Israel took the corridor last Wednesday, Mr. Moussa was on the air, fulminating against social media users who said Egypt looked weak for allowing the seizure. He linked such “allegations” to the Muslim Brotherhood, the political Islamist group that Egypt has long demonized as a terrorist organization, of which Hamas is an offshoot.

“The Philadelphi Corridor is not Egyptian territory,” Mr. Moussa insisted in a nine-minute segment devoted to the issue, displaying a giant map. “It’s Palestinian territory. It doesn’t belong to us. Let me show you our borders.”

Isabel Kershner contributed reporting.