By 9 a.m. local time, the military had begun dropping leaflets in eastern Rafah ordering people to evacuate, and it said it would also notify people by text messages, phone calls and broadcasts in Arabic. An Israeli military spokesman would not say if or when troops would enter the city, but described the evacuation as “part of plans to dismantle Hamas” and to bring back hostages taken on Oct. 7.

Since the start of Israel’s ground offensive in Gaza last year, about a million people have fled to Rafah, the southernmost city in the enclave, where they have been living in dire conditions. Israel has told civilians in many parts of Gaza to evacuate from their homes for safety since the start of the war. But in many instances the places Israel said would be safe for Gazans were also targeted by Israeli airstrikes.

Israel’s closest allies, including the United States, have been urging it not to send troops into Rafah, saying such an operation would take a heavy toll on civilians. But Prime Minister Benjamin Netanyahu has repeatedly rejected those calls, saying Israel needs to defend itself and eliminate Hamas, which attacked Israel on Oct. 7.

The evacuation order came a day after officials said that months of talks over a cease-fire and the release of hostages had hit an impasse, with Israel and Hamas still sharply at odds over the duration of any truce. Hamas wants a permanent cease-fire while Mr. Netanyahu has expressed openness to only a temporary halt in the fighting and has said Israel would invade Rafah with or without an agreement.

Salama Marouf, the head of the Hamas-run Gaza government media office, said in a statement on Monday that the evacuation order showed that Israel “went into truce negotiations deceptively without abandoning the idea of ​​a broad aggression against Rafah.” He said the announcement was “a real test of the seriousness” of the countries that had warned against an invasion of the city.

On Sunday, Mr. Netanyahu repeated his promises to destroy Hamas, vowing in English, in a speech marking Israel’s Holocaust Remembrance Day, that Israel “will defeat our genocidal enemies.”

About two weeks ago, the Israeli authorities said that before they moved on Rafah, they would expand a humanitarian zone in nearby Al-Mawasi where civilians could shelter. On Monday, the Israeli military said that it had done so, and that the zone had field hospitals, tents and larger supplies of food, water and medicines.

The military is not calling for a “wide-scale evacuation of Rafah,” Nadav Shoshani, the military spokesman, said on Monday. “This is a very specific scoped operation at the moment to move people out of harm’s way.” The order applied both to residents of Rafah and to those who fled there from elsewhere in Gaza.

Previous Israeli evacuation orders offer no clear clues about when a ground operation in Rafah might start. Israel began instructing civilians to leave northern Gaza and move south for their own safety around two weeks before its invasion began on Oct. 27.

Days before launching an invasion of the city of Khan Younis in central Gaza in early December, Israel again urged civilians to move south. On that occasion, they also designated certain areas of the city to be safe, making announcements and dropping leaflets to convey the information.

In both cases, civilians reported that obeying the orders was fraught with peril, leaving them with agonizing decisions and often no safe options. Northern Gaza was under heavy bombardment in the weeks before the invasion, while people in Khan Younis said that the evacuation orders were inadequately communicated and sometimes left them with just hours to escape.

UNRWA, the U.N. agency that aids Palestinian refugees, said on Monday that it would not evacuate its staff from Rafah and would continue to provide humanitarian aid to those who have taken refuge there.

“An Israeli military offensive will lead to an additional layer of an already unbearable tragedy for the people in Gaza,” Philippe Lazzarini, the agency’s commissioner general, said on social media.

Isabel Kershner, Myra Noveck and Liam Stack contributed reporting.

But Mr. Netanyahu has remained defiant.

On Sunday, he spoke at Yad Vashem, Israel’s Holocaust memorial in Jerusalem, to mark the national Holocaust remembrance day. Hamas’s Oct. 7 attack, he said, was not a “Holocaust” — not because Hamas did not have the intention to destroy Israel but because of its inability to do so. About 1,200 people were killed and more than 200 were taken hostage that day, Israeli authorities say. Hamas’s intention, Mr. Netanyahu said, was the same as that of the Nazis.

In his speech, which lasted for about 15 minutes and was largely in Hebrew, Mr. Netanyahu rejected accusations that Israel was committing genocide in the Gaza Strip. Since the beginning of the war, Gazan authorities say Israeli troops have killed more than 34,000 people, many of them women and children, though the statistics do not differentiate between civilians and combatants.

Mr. Netanyahu said that Israel’s military does everything it can to avoid harming civilians and that it has allowed aid to flow through to Gaza to avoid a humanitarian crisis. A United Nations official recently said that parts of Gaza are experiencing “full-blown famine.”

Mr. Netanyahu made a point to say a few words in English that were aimed at the international community. He invoked the Holocaust in asserting Israel’s right to defend itself, with or without international support.

“If Israel is forced to stand alone, Israel will stand alone,” he said. “But we know we are not alone because countless decent people around the world support our just cause. And I say to you, we will defeat our genocidal enemies. Never again is now!”

On Monday morning after his speech, the Israeli military gave the strongest signal yet that it was going to invade Rafah as it asked tens of thousands of Gazans to evacuate from the city.

But the setback over the weekend meant Palestinians living in miserable conditions in Gaza would not experience an imminent reprieve and the families of hostages held by militants would have to wait longer for the freedom of their loved ones.

The main obstacle in the talks was the duration of a cease-fire, with Hamas demanding it be permanent and Prime Minister Benjamin Netanyahu of Israel expressing openness to only a temporary halt in the fighting.

Hamas blamed the lack of progress on Mr. Netanyahu, who vowed again in recent days that the Israeli army will invade Rafah, the southernmost town in the Gaza Strip, with or without an agreement.

“We were very close, but Netanyahu’s narrow-mindedness aborted an agreement,” Mousa Abu Marzouk, a senior Hamas official, said in a phone interview.

Mr. Netanyahu has for weeks declared his intention to stage a ground offensive aimed at Rafah, where about a million Palestinians have been sheltering. The Biden administration has been pressing Israel to refrain from undertaking a major operation in the city.

On Sunday, Hamas fired roughly 10 rockets from the area of the Rafah border crossing, killing three soldiers near the Kerem Shalom crossing, according to Israel’s military. Rocket attacks by Hamas have been relatively rare in recent months, and Israel said it had responded with airstrikes targeting the site of the launches.

The Israeli official who spoke on the condition of anonymity said that Israel and Hamas were closer to a deal a couple of days ago, but that Mr. Netanyahu’s statements about Rafah had compelled Hamas to harden its demands in an attempt to ensure that Israeli forces won’t enter the city. Hamas, the official said, was now seeking further guarantees that Israel would not implement only part of an agreement, and then resume fighting.

The official lamented that Hamas and Israel had shifted gears to playing a “blame game.”

Two U.S. officials, who spoke on the condition of anonymity, pushed back on the notion the talks were at an impasse, suggesting that parties were still reviewing details of the most recent proposals.

Mr. Netanyahu and the United States have been contending that Hamas was holding up an agreement. On Sunday, Mr. Netanyahu said he would not agree to the complete withdrawal of Israeli forces from Gaza and an end to the war. Countenancing such demands, he said, would allow Hamas to re-establish control over Gaza, rebuild their military capabilities, and threaten communities throughout Israel.

“It is Hamas that is holding up the release of our hostages,” he said. “We are working in every possible way to free the hostages; this is our top priority.”

An Israeli delegation never made it to Cairo for the latest round of talks. The Israeli official said that Israel had sought a written response to its latest proposal from Hamas before dispatching a delegation, but that the group never conveyed one.

Mr. Abu Marzouk said Hamas had wanted Israel to be present at the talks in Cairo, where they could have worked through mediators to clarify “vague” points in the latest Israeli offer, including on the duration of a cease-fire.

“The cease-fire needs to be permanent and fixed,” he said.

Mr. Abu Marzouk was the only one of the officials who spoke about the talks to allow the use of his name. The others spoke on the condition of anonymity to discuss the sensitive subject or because they were not authorized to speak to the press.

Hamas, Mr. Abu Marzouk said, thought that Mr. Netanyahu wanted an agreement that would permit Israel to invade Rafah after its hostages are released.

“This is Netanyahu’s plan,” he said.

A technical team from the Qatari foreign ministry also left the Egyptian capital on Sunday, two officials briefed on the talks said. Bill Burns, the director of the Central Intelligence Agency, met with Qatari Prime Minister Mohammed bin Abdulrahman Al Thani in Doha on Sunday to discuss getting the talks back on track, one of the officials said.

On Monday, Hamas’s political leadership will convene in Doha to discuss what unfolded in Cairo over the past two days, but the group intended to continue participating in negotiations with “positivity,” said one of the senior Hamas officials, who spoke on the condition of anonymity.

A report in Al-Qahera News, an Egyptian state-owned television channel, said that a Hamas delegation would return to Cairo on Tuesday, but the senior Hamas official said that the group hadn’t made a decision yet.

Peter Baker and Michael Crowley contributed reporting to this article.

But invoking national security as the basis for barring a news organization from operating in a country is “incredibly vague” and “way outside the bounds of democratic norms,” said Joel Simon, director of the Journalism Protection Initiative at the Craig Newmark Graduate School of Journalism at the City University of New York.

Jameel Jaffer, executive director of the Knight First Amendment Institute at Columbia University, said that closing off a country to information, news and ideas from abroad has long been a hallmark of repressive governments.

“The legitimacy of any democracy turns in part on its citizens having unrestricted access to foreign media,” Mr. Jaffer said.

Some free speech advocates acknowledged that the United States seems to be pulling back from its role as a champion of information freedom. Washington is moving to ban TikTok, the popular social media app with a Chinese parent company, unless it is sold to American investors.

But Israel, they said, is a different case. Shutting down Al Jazeera is the latest step in “a broad attack on press and speech freedom” by the Israeli government, said Genevieve Lakier, a professor at the University of Chicago Law School who writes about freedom of speech. Israel’s actions, she added, are “inconsistent with a commitment to democratic values.”

Carlos Martinez de la Serna, program director of the Committee to Protect Journalists, said in a statement that Israel’s move “sets an extremely alarming precedent for restricting international media outlets working in Israel.” He called on the Israeli government to reverse course and “allow Al Jazeera and all international media outlets to operate freely in Israel, especially during wartime.”

But there are concerns that Israel may go in the other direction. “Is Al Jazeera a test case?” asked Seth Stern, director of advocacy at the Freedom of the Press Foundation. “Will Israel start going after other news outlets that are not to the government’s liking?”