Israeli tanks seized control of Gaza's vital Rafah border crossing on Tuesday as Israel brushed off urgent warnings from close allies and moved into the southern city even as cease-fire negotiations with Hamas remained on a knife's edge.

The U.N. warned of a potential collapse of the flow of aid to Palestinians from the closure of Rafah and the other main crossing into Gaza, Kerem Shalom, at a time when officials say the northern part of the enclave is already experiencing "full-blown famine."

The Israeli foray overnight came after hours of whiplash in the Israel-Hamas war, with the militant group on Monday saying it accepted an Egyptian-Qatari mediated cease-fire proposal. Israel, however, insisted the deal did not meet its core demands.

The high-stakes diplomatic moves and military brinkmanship left a glimmer of hope alive — if only barely — for a deal to bring at least a pause in the war, which as it marked its 7-month point Tuesday, has killed more than 34,700 Palestinians, according to local health officials, and has devastated the Gaza Strip.

The incursion appeared to be short of the full-fledged offensive into Rafah that Israel has planned, and it was not immediately known if it would be expanded. The looming operation threatens to widen a rift between Israel and its main backer, the United States, which says it is concerned over the fate of around 1.3 million Palestinians crammed into the city.

U.S. President Joe Biden warned Israeli Prime Minister Benjamin Netanyahu again on Monday against launching an invasion of the city after Israel ordered 100,000 Palestinians to evacuate from parts of Rafah.

Cheers of joy overnight among Rafah's Palestinians over Hamas' acceptance of the cease-fire turned to fear Tuesday. Families fled in a steady stream out of Rafah's eastern neighborhoods on foot or in vehicles and donkey carts piled with mattresses and supplies. Children watched as parents disassembled tents in the sprawling camps that have filled Rafah for months to move to their next destination — which for many remained uncertain.

"Netanyahu only cares about coming out on top. He doesn't care about children. I don't think he'll agree" to a deal, said Najwa al-Saksuk as her family packed up. Israeli strikes rang out and raised plumes of black smoke.

The Israeli 401st Brigade entered the Gaza side of the Rafah crossing early Tuesday, the Israeli military said, taking "operational control" of it. Footage released by the military showed Israeli flags flying from tanks that seized the area. It also said that ground troops and airstrikes targeted suspected Hamas positions in Rafah.

The military claimed it had intelligence the crossing was "being used for terrorist purposes," though it did not immediately provide evidence. It said Hamas fighters near the crossing launched a mortar attack that killed four Israeli troops near Kerem Shalom on Sunday and that more mortars and rockets were fired from the area on Tuesday.

The Rafah crossing with Egypt and the Kerem Shalom crossing with Israel are critical points of entry for food, medicine and other supplies keeping Gaza's population of 2.3 million alive. They have been closed for at least the past two days, though the smaller Erez crossing between Israel and northern Gaza continues to operate.

Israeli authorities denied the U.N. humanitarian affairs office access to Rafah crossing Tuesday, its spokesman Jens Laerke said, warning that the disruption could break the fragile aid operation. All fuel for aid trucks and generators comes through Rafah, and Laerke said they have a "very, very short buffer of about one day of fuel."

"If no fuel comes in for a prolonged period of time, it would be a very effective way of putting the humanitarian operation in its grave," he said.

Israeli strikes and bombardment across Rafah overnight killed at least 23 Palestinians, including at least six women and five children, according to hospital records.

Mohamed Abu Amra said his wife, two brothers, sister and niece were killed when a strike flattened their home as they slept. "We did nothing. ... We don't have Hamas," he said. "We found fire devouring us. The house was turned upside down."

Egypt's Foreign Ministry condemned the seizure of the crossing, calling it "a dangerous escalation."

Egypt has previously warned that any seizure of Rafah — which is supposed to be part of a demilitarized border zone — or an attack that forces Palestinians to flee over the border into Egypt would threaten the 1979 peace treaty with Israel that's been a linchpin for regional security.

Netanyahu has said an offensive to take Rafah — which Israel says is Hamas' last major stronghold in Gaza — is crucial to the goal of destroying Hamas after its Oct. 7 attack on southern Israel that triggered the war.

In that unprecedented Hamas raid, militants killed some 1,200 people and took around 250 others as hostages back to Gaza. Israeli critics say Netanyahu is concerned about his government's survival, since hard-line partners in his coalition could bolt if he signs onto a deal before a Rafah invasion.

As Israel announced it would push ahead with Rafah operations, it said the cease-fire proposal that Hamas agreed to did not meet its "core demands." But it said it would send a delegation to Egypt to continue negotiations. An Egyptian official said delegations from Hamas and Qatar arrived in Cairo on Tuesday.

An Egyptian official and a Western diplomat said the draft Hamas accepted had only minor changes in wording from a version the U.S. had earlier pushed for with Israeli approval. The changes were made in consultation with CIA chief William Burns, who embraced the draft before sending it to the Palestinian group, the diplomat and official said, speaking on condition of anonymity to discuss the internal deliberations.

The White House said Burns was discussing the Hamas response with the Israelis and other regional officials.

According to a copy released by Hamas after it acceptance, the proposal outlines a phased release of the hostages alongside the gradual withdrawal of Israeli troops from the entire enclave and ending with a "sustainable calm," defined as a "permanent cessation of military and hostile operations." Hamas is believed to still hold around 100 Israelis captive, along with the bodies of around 30 others.

In the first, 42-day stage of the cease-fire, Hamas would release 33 hostages — including women, children, older adults and the ill — in return for the release of hundreds of Palestinians in Israeli prisons, and Israeli forces would withdraw from parts of Gaza. The parties would then negotiate the terms of the next stage, under which the remaining civilian men and soldiers would be released, while Israeli forces would withdraw from the rest of Gaza.

Hamas has demanded an end to the war and complete Israeli withdrawal in return for the release of all hostages. Publicly, Israeli leaders reject that trade-off, vowing the war will continue until the hostages are all released — and Hamas is destroyed.