Live Updates: Israeli Tanks Enter Rafah and Take Control of Border Crossing

Prime Minister Benjamin Netanyahu is facing pressure to agree to a cease-fire with Hamas that is backed by the United States and Arab nations and that would secure the release of hostages still being held in Gaza. His government said that it would send negotiators to Cairo on Tuesday.

The Egyptian state-owned television channel Al Qahera reported that sporadic fighting could be heard around the Rafah crossing and that humanitarian aid through it had stopped. United Nations officials said that Israeli troops had now “choked off” both the Rafah and Kerem Shalom crossings, the two main routes for getting aid into Gaza and warned that the humanitarian crisis in the enclave would worsen.

The Israeli military called Tuesday’s incursion “a very precise” counterterrorism operation and declined to say how long it planned to stay in Rafah. Troops found three tunnel shafts in the area near the crossing, and about 20 militants were killed during the operation, it said in a statement, without offering evidence. Israel has long viewed Gaza’s border with Egypt as a main route for smuggling arms into the coastal enclave.

Here’s what else to know:

• The incursion on Tuesday and airstrikes the day before are an escalation in the fighting after Israel withdrew most of its forces from the Gaza Strip in April. Israel’s campaign has forced almost all of Gaza’s population to flee their homes. More than a million have gone to Rafah, where large numbers of people have been living in squalid tent camps. On Monday, Israel told more than 100,000 Gazans in eastern Rafah to flee ahead of airstrikes; it was not immediately clear how many were able to leave.

• On Monday evening, António Guterres, the U.N. secretary general, said again that “a ground invasion in Rafah would be intolerable because of its devastating humanitarian consequences and because of its destabilizing impact in the region.”

• An invasion of Rafah has been a point of tension for Mr. Netanyahu and his closest international allies. The United States has warned him not to launch an invasion without a credible plan to protect Rafah’s population. President Biden spoke by phone with Mr. Netanyahu on Monday and again urged against an offensive.

• Ground and air forces were also operating overnight in a neighborhood of eastern Rafah near the border crossing, the military said. It did not specify the location of the tunnel shafts or where the fighters had been killed.

Aaron Boxerman contributed reporting.

The Qassam Brigades, Hamas’s armed wing, said it had fired on gatherings of soldiers in the border region between Israel and Gaza.

The two officials said the response from Hamas was a serious one, and that it was now up to Israel to decide whether to enter into an agreement. The proposal, they said, calls for Hamas to free hostages — women, the elderly and those in need of medical treatment — in return for a 42-day cease-fire and the release of a much larger number of Palestinian prisoners. Israel had sought 33 hostages, but it is not clear how many women and elderly are still alive, and the first tranche could end up including remains.

That would be the first of three phases of reciprocal actions from each side. In the second phase, the two sides would work toward reaching a “sustainable calm,” which would involve the release of more hostages, the officials said. Both officials acknowledged that the warring parties would likely clash over the definition of “sustainable calm.”

One of the officials, in the Middle East, said that Hamas viewed the term as an end to the war, with Israel halting its military actions and withdrawing troops from Gaza. The officials said that Israel’s prime minister, Benjamin Netanyahu, was expected to push back against that definition.

One official said that the negotiating parties agreed to the term “sustainable calm” weeks ago, after Israel objected to any reference to a “permanent cease-fire.” Israeli officials have consistently said they oppose any agreement that explicitly calls for that or for an end to the war.

Mr. Burns has been the main representative for the United States in the negotiations, and he is in the region to work on the proposals and counterproposals. Qatari and Egyptian mediators spoke with him on Monday about the changes that Hamas was ready to accept, the two officials said. Hamas said that Arab mediators had put forward the changes, but one official said that Hamas had suggested them. Mr. Burns is expected to attend the talks in Cairo on Tuesday.

The Israeli prime minister’s office said that while the new proposal failed to meet Israel’s demands, the country would still send a working-level delegation to talks in hopes of reaching an acceptable deal. A U.S. official said the purpose of the talks in Cairo was to negotiate the amendments proposed by Hamas and talk through remaining issues.

Qatar’s Foreign Ministry said that a Qatari delegation would also attend the talks on Tuesday, and expressed “hope that the talks will culminate in reaching an agreement for an immediate and permanent” cease-fire, an exchange of hostages and prisoners, and a “sustainable” flow of aid into all of Gaza.

Israel announced on Monday that its war cabinet had voted unanimously to continue with its military action in Rafah in order to exert pressure on Hamas. That announcement and the start of any offensive in the city could jeopardize the prospects for an agreement. Mr. Netanyahu said last week that he would carry out an offensive in Rafah “with or without” an agreement.

U.S. officials say they oppose any such operation without a proper plan from Israel to mitigate civilian casualties and a humanitarian crisis. One U.S. official said the strikes that the Israeli military carried out in eastern Rafah on Monday appeared to be part of a smaller operation, and not necessarily the opening moves of a larger assault. More than one million Palestinians have sought shelter in Rafah as they fled other parts of Gaza under attack by Israel.

Adam Rasgon contributed reporting from Jerusalem.

Here is a look at the recent dizzying turn of events.

Monday, April 29

Israeli officials, offering a hint of hope for a deal, said that their negotiators had reduced the number of hostages they wanted Hamas to release during the first phase of a truce.

Thursday, May 2

A Hamas leader said that the group would soon send a delegation to Cairo to “complete ongoing discussions” on a cease-fire deal.

Saturday, May 4

With talks underway, a senior Hamas official said in a text message that the group’s representatives had arrived in Cairo for the talks, “with great positivity” toward the latest proposal.

Sunday, May 5

The talks — which are held indirectly, through mediators — hit an impasse, and Hamas said its delegation had left Cairo. An Israeli official described the negotiations as in “crisis.”

Late in the day, Hamas launched rockets at a border crossing between Gaza and Israel, killing four Israeli soldiers. Israel stepped up its attacks in Gaza.

Monday, May 6

Hamas said it accepted the terms of a cease-fire — not as laid out in Israel’s proposal, but drawn from one put forth by Egypt and Qatar.

The timing appeared noteworthy. The announcement was made after Israel had ordered people to evacuate from some areas in Rafah, a sign that Israeli forces might be close to launching a long-anticipated invasion of the refugee-packed city. Late in the day, the Israeli military said it was carrying out “targeted strikes” on in eastern Rafah.

The strikes may prove to be an attempt to turn up the pressure on Hamas negotiators. Late in the day, in keeping with a week of contradictory signals, the Israeli prime minister’s office said that Hamas’s latest cease-fire proposal was unsatisfactory.

Then it said would send a working-level delegation back to the talks in Cairo anyway.

But analysts say it would also be a necessary step toward the total victory over Hamas that Mr. Netanyahu has pledged — however elusive that may prove — and would mollify the hard-liners in the government coalition that keeps him in power.

Critics had accused Mr. Netanyahu of scuttling the latest round of hostage talks, which appeared to have stalled over the weekend. The two sides were mainly stuck over Hamas’s demand that Israel commit to a permanent cease-fire as part of any deal, according to Israeli and Hamas officials, and over Mr. Netanyahu’s insistence on a Rafah invasion and willingness to commit to only a temporary pause in the seven-month war.

Negotiators were hoping to make some progress by allowing for a degree of ambiguity, at least in the early stages of a phased deal. But Mr. Netanyahu made it patently clear over the weekend, in a series of statements, that he was not willing to give up on Rafah or commit to an end to the war, and on Monday, when Hamas said it would agree to a plan set out by Egypt and Qatar, Israeli forces stepped up their strikes on the city.

One Israeli official, who spoke on the condition of anonymity, said on Sunday that Mr. Netanyahu’s statements about Rafah and the continuation of the war had compelled Hamas to harden its demands. At the same time, a Hamas rocket attack launched from near the Rafah crossing between Gaza and Egypt on Sunday, which killed four soldiers in Israel, showed that Hamas was still capable of mounting damaging attacks from its last redoubt.

Pushing back against the accusations, Mr. Netanyahu’s office issued a statement on Monday calling the claims that he, and not Hamas, had torpedoed the deal “an absolute lie and willful deception of the public.”

On the contrary, the statement said, Hamas had not “moved a millimeter from its extreme demands, which no Israeli government could accept.”

By Monday evening, when Hamas announced that there was a truce plan it could agree to, Israeli analysts were crediting the military’s moves in Rafah with having pressured Hamas into seeking a deal.

But the meaning of going into Rafah is also open to interpretation. The Israeli military portrayed Monday’s call for a “temporary” evacuation of eastern Rafah as “limited in scope,” suggesting that it is not a precursor to an imminent invasion of the whole city.

That raised questions about Israel’s ability to destroy the last four Hamas battalions that it says are in Rafah and must be defeated.

Alon Pinkas, a former Israeli consul-general in New York, said of Mr. Netanyahu after seven months of war: “He’s out of options.”

“We are not going to see Hamas raise a white flag,” Mr. Pinkas said. Yet Mr. Netanyahu, he added, “has turned Rafah into some kind of Stalingrad.”

Adam Rasgon contributed reporting.

As Israeli forces carried out strikes in eastern Rafah, the prime minister’s office said that the war cabinet had decided unanimously that Israel would continue with its military actions in the city to exert pressure on Hamas. The decision, the office said, sought to advance all of Israel’s war aims, including freeing hostages.

Khalil al-Hayya, a senior Hamas official, said in an interview with Al Jazeera that the proposal Hamas was willing to accept included three phases, of 42 days each, and stressed that its main goal was a permanent cease-fire.

Ismail Haniyeh, the head of Hamas’s political wing, first described Hamas’s new position in a post on the group’s Telegram channel at 7:36 p.m. in Israel. His statement came hours after Israel had ordered people in part of Rafah, the southernmost city in Gaza, to evacuate before a promised offensive there, and a day after Hamas fired rockets near the Kerem Shalom crossing in the border region between Israel and southern Gaza, killing four soldiers.

Mr. Haniyeh said he had told the Qatari prime minister and the chief of Egypt’s General Intelligence Service that Hamas had accepted “their proposal.” There was no immediate comment from Egypt.

Matthew Miller, the State Department spokesman, confirmed that Hamas had “issued a response” and that the United States was reviewing it with partners in the region.

Hamas negotiators had left Cairo on Sunday after talks hit an impasse and they failed to reach an agreement with mediators on Israel’s most recent offer.

The main stumbling block in the indirect negotiations mediated by Qatar and Egypt has been the length of the cease-fire. Hamas has demanded a permanent cease-fire, which would in effect end the seven-month war, while Israel wants a temporary halt in fighting that would allow for the exchange of hostages held in Gaza for Palestinian prisoners.

Mr. al-Hayya, who has been leading Hamas delegations at in-person talks in Cairo, said the new offer also included a complete Israeli withdrawal from Gaza, the return of displaced people to their homes and a “real and serious” swap of hostages for Palestinian prisoners.

In its most recent proposal, Israel made some concessions, including agreeing to the return of displaced Palestinians to northern Gaza and reducing the number of hostages it would accept being freed in the initial phase of an agreement.

The Israeli military’s chief spokesman, Rear Adm. Daniel Hagari, said at a news briefing on Monday evening: “We examine each response and reply in a very serious matter, and maximize every opportunity in the negotiations to secure the release of the hostages as a core mission.” But he said that at the same time, Israeli forces would “continue operating” in Gaza.

The Israeli military ordered the evacuation of over 100,000 Palestinians from parts of Rafah on Monday morning. Israeli leaders have vowed for months to invade the city in order to root out Hamas forces there, prompting international concern for the safety of the 1.4 million people sheltering there.

Michael Crowley and Aaron Boxerman contributed reporting.