The United States believes the remaining differences between Israel and Hamas can be bridged in negotiations over the Palestinian militant group’s latest ceasefire proposal, as talks resume in Cairo on Wednesday.

Israeli forces on Tuesday seized the main border crossing between Gaza and Egypt in Rafah, the southern Gaza city where more than one million displaced Palestinians have sought shelter during Israel’s seven-month-old offensive. This cut off a vital route for aid into the tiny enclave, where hundreds of thousands of people are homeless and hungry.

In Cairo, all five delegations participating in ceasefire talks on Tuesday – Hamas, Israel, the U.S., Egypt and Qatar – reacted positively to the resumption of negotiations, and meetings were expected to continue on Wednesday morning, two Egyptian sources said.

CIA Director Bill Burns was to travel from Cairo to Israel later on Wednesday to meet Israeli Prime Minister Benjamin Netanyahu and Israeli officials, a source familiar with his travel said.

Israel on Monday declared that a three-phase proposal approved by Hamas was unacceptable because terms had been softened.

White House spokesperson John Kirby said Hamas presented a revised proposal, and the new text suggests the remaining gaps can “absolutely be closed.” Speaking on Tuesday, he declined to specify what those were.

Since the only pause in the conflict so far, a week-long ceasefire in November, the two sides have been blocked by Hamas’ refusal to free more Israeli hostages without a promise of a permanent end to the conflict and Israel’s insistence that it would discuss only a temporary halt.

Israeli army footage on Tuesday showed tanks rolling through the Rafah crossing complex between Gaza and Egypt, and the Israeli flag raised on the Gaza side. Israel says Rafah is Hamas fighters’ last stronghold.

Hamas official Osama Hamdan, speaking to reporters in Beirut on Tuesday, warned that if Israel’s military aggression continued in Rafah, there would be no truce agreement.

Israel’s military said it was conducting a limited operation in Rafah to kill fighters and dismantle infrastructure used by Hamas, which runs Gaza. It told civilians, many of whom were previously displaced from other parts of Gaza earlier in the conflict, to go to an “expanded humanitarian zone” some 20 km (12 miles) away.

U.N. Secretary-General Antonio Guterres appealed to Israel and Hamas to spare no effort to agree to a truce. “Make no mistake – a full-scale assault on Rafah would be a human catastrophe,” Guterres said.

In Geneva, U.N. humanitarian office spokesperson Jens Laerke said “panic and despair” were gripping the people in Rafah.

HEAVY SHELLING IN RAFAH

Residents reported heavy tank shelling on Tuesday evening in some areas of eastern Rafah. A Rafah municipal building caught fire after Israeli shelling, and one Palestinian was killed and several wounded, medics said. An Israeli strike also killed two Palestinians on a motorcycle, they said.

Health officials said Abu Yousef Al-Najar, the main hospital in Rafah, closed on Tuesday after heavy bombardment nearby led medical staff and around 200 patients to flee.

“They have gone crazy. Tanks are firing shells and smoke bombs cover the skies,” said Emad Joudat, 55, a Gaza City resident displaced in Rafah.

The U.N. and other international aid agencies said the closing of the two crossings into southern Gaza – Rafah and Israeli-controlled Kerem Shalom – virtually cut the enclave off from outside aid and very few stores were available inside.

Families have been crammed into tented camps and makeshift shelters, suffering from shortages of food, water, medicine and other essentials.

Red Crescent sources in Egypt said shipments had completely halted. “These crossings are a lifeline… They need to be reopened without any delay,” Philippe Lazzarini, head of U.N. aid agency UNRWA, said on X.

The White House said it had been told the Kerem Shalom crossing would re-open on Wednesday and fuel deliveries through Rafah would resume then too.

According to Hamas officials, a draft proposal and an official briefed on the talks, the proposal that Hamas approved on Monday included a first phase with a six-week ceasefire, an influx of aid to Gaza, the return of 33 Israeli hostages, alive or dead, and release by Israel of 30 detained Palestinian children and women for each released Israeli hostage.

Critics of the Gaza war have urged U.S. President Joe Biden to pressure Israel to change course. The U.S., Israeli’s closest ally and main weapons supplier, has delayed some arms shipments to Israel for two weeks, according to four sources on Tuesday.

The White House and Pentagon declined comment, but this would be the first such delay since the Biden administration offered its full support to Israel after Hamas’ Oct. 7 attack.

Israel’s offensive has killed 34,789 Palestinians, most of them civilians, in the conflict, the Gaza Health Ministry said.

The war began when Hamas militants attacked Israel on Oct. 7, killing about 1,200 people and abducting about 250 others, of whom 133 are believed to remain in captivity in Gaza, according to Israeli tallies.