Hamas said Monday it accepted an Egyptian-Qatari cease-fire proposal, but Israel said the deal did not meet its core demands and it was pushing ahead with an assault on the southern Gaza city of Rafah. Still, Israel said it would continue negotiations.

The high-stakes diplomatic moves and military brinkmanship left a glimmer of hope alive — but only barely — for an accord that could bring at least a pause in the 7-month-old war that has devastated the Gaza Strip. Hanging over the wrangling was the threat of an all-out Israeli assault on Rafah, a move the United States strongly opposes and that aid groups warn will be disastrous for some 1.4 million Palestinians taking refuge there.

Hamas's abrupt acceptance of the cease-fire deal came hours after Israel ordered an evacuation of some 100,000 Palestinians from eastern neighborhoods of Rafah, signaling an invasion was imminent.

The Israeli military said it was conducting “targeted strikes” against Hamas in eastern Rafah. Soon after, Israeli tanks entered Rafah, reaching as close as 200 meters (yards) from Rafah’s crossing with neighboring Egypt, a Palestinian security official and an Egyptian official said. Both spoke on condition of anonymity because they were not authorized to talk to the media. The reported incursion came a day after Hamas militants killed four Israeli soldiers in a mortar attack that Israel said originated near the Rafah crossing.

The Egyptian official said the operation appeared to be limited. The Associated Press could not independently verify the scope of the operation.

Israeli airstrikes also hit elsewhere in Rafah late Monday, killing at least five people, including a child and a woman, hospital officials said.

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The Israeli military declined to comment.

Shortly after Hamas said it had accepted the Egyptian-Qatari truce proposal, Israel's War Cabinet decided to continue the Rafah operation, Prime Minister Benjamin Netanyahu 's office said. It also said that while the proposal Hamas agreed to “is far from meeting Israel’s core demands,” it would send negotiators to Egypt to work on a deal. Late Monday, Qatar announced it was sending a team to Egypt as well.

President Joe Biden spoke with Netanyahu and reiterated U.S. concerns about an invasion of Rafah. U.S. State Department spokesman Matthew Miller said American officials were reviewing the Hamas response “and discussing it with our partners in the region.”

It was not immediately known if the proposal Hamas agreed to was substantially different from one that U.S. Secretary of State Antony Blinken pressed the militant group to accept last week, which Blinken said included significant Israeli concessions.

An American official said the U.S. was examining whether what Hamas agreed to was the version signed off on by Israel and international negotiators or something else.

Egyptian officials said that proposal called for a cease-fire of multiple stages starting with a limited hostage release and partial Israeli troop pullbacks within Gaza. The two sides would also negotiate a “permanent calm” that would lead to a full hostage release and greater Israeli withdrawal out of the territory, they said.

Hamas sought clearer guarantees for its key demand of an end to the war and complete Israeli withdrawal in return for the release of all hostages, but it wasn't clear if any changes were made.

Israeli leaders have repeatedly rejected that trade-off, vowing to keep up their campaign until Hamas is destroyed after its Oct. 7 attack on Israel that triggered the war.

Netanyahu is under pressure from hard-line partners in his coalition who demand an attack on Rafah and could collapse his government if he signs a deal. But he also faces pressure from the families of hostages to reach a deal for their release. They say that time is running out to bring their loved ones home safely, and a ground operation would further endanger them.

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Thousands of Israelis rallied around the country Monday night calling for an immediate agreement. About 1,000 protesters swelled near the defense headquarters in Tel Aviv. In Jerusalem, about 100 protesters marched toward Netanyahu's residence with a banner reading, “The blood is on your hands."

Israel says Rafah is the last significant Hamas stronghold in Gaza, and Netanyahu said Monday that the offensive against the city was vital to ensuring the militants can’t rebuild their military capabilities.

But he faces strong American opposition. Miller said Monday the U.S. has not seen a credible plan to protect Palestinian civilians. “We cannot support an operation in Rafah as it is currently envisioned,” he said.

The looming operation has raised global alarm. Aid agencies have warned that an offensive will bring a surge of more civilian deaths in an Israeli campaign that has already killed over 34,000 people and devastated the territory. It could also wreck the humanitarian aid operation based out of Rafah that is keeping Palestinians across the Gaza Strip alive, they say.

Israeli leaflets, text messages and radio broadcasts ordered Palestinians to evacuate eastern neighborhoods of Rafah, warning that an attack was imminent and anyone who stays “puts themselves and their family members in danger.”

The military told people to move to an Israel-declared humanitarian zone called Muwasi, a makeshift camp on the coast. It said Israel has expanded the size of the zone and that it included tents, food, water and field hospitals.

It wasn’t immediately clear, however, if that was already in place.

Around 450,000 displaced Palestinians already are sheltering in Muwasi. The U.N. agency for Palestinian refugees, known as UNRWA, said it has been providing them with aid. But conditions are squalid, with few sanitation facilities in the largely rural area, forcing families to dig private latrines.

The evacuation order left Palestinians in Rafah wrestling with having to uproot their families once again for an unknown fate, exhausted after months living in sprawling tent camps or crammed into schools or other shelters in and around the city. Israeli airstrikes on Rafah early Monday killed 22 people, including children and two infants.

Mohammed Jindiyah said that at the beginning of the war, he tried to hold out in his home in northern Gaza under heavy bombardment before fleeing to Rafah.

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He is complying with Israel's evacuation order this time, but was unsure whether to move to Muwasi or elsewhere.

“We are 12 families, and we don’t know where to go. There is no safe area in Gaza,” he said.

Sahar Abu Nahel, who fled to Rafah with 20 family members, including her children and grandchildren, wiped tears from her cheeks, despairing at a new move.

“I have no money or anything. I am seriously tired, as are the children,” she said. “Maybe it’s more honorable for us to die. We are being humiliated.”

The war was sparked by the unprecedented Oct. 7 raid into southern Israel in which Palestinian militants killed around 1,200 people, mostly civilians, and abducted some 250 hostages. After exchanges during a November cease-fire, Hamas is believed to still hold about 100 hostages as well the bodies of around 30 others.