Hamas official Osama Hamdan, speaking to reporters in Beirut, warned that if Israel's military aggression continued in Rafah, there would be no truce agreement.
The Palestinian militant group accused Israel of undermining ceasefire efforts in the seven-month-long war that has laid waste to Gaza and left hundreds of thousands of its people homeless and hungry.
The truce comments came as Israel invaded Rafah, a southern Gazan city where more than one million displaced Palestinian civilians have sought shelter from Israel's offensive throughout the tiny territory.
The US says Hamas and Israel can close the gaps in negotiating a ceasefire in Gaza. (AP PHOTO)
White House spokesperson John Kirby on Tuesday said Hamas offered amendments on Monday to an Israeli proposal aimed at ending the impasse. The deal text, as amended, suggests the remaining gaps can "absolutely be closed", he said. He declined to specify what those were.
Israel on Monday said a three-phase proposal that Hamas approved was unacceptable.
Kirby said mediators from Qatar and Egypt along with US and Israeli officials were gathering in Cairo. Hamas separately said its delegation was in Cairo as well.
Israel's seizure of the Rafah crossing came despite weeks of calls that the US, other nations and international bodies hoped would deter a big offensive in the Rafah area - which Israel says is Hamas fighters' last stronghold.
Israeli army footage showed tanks rolling through the Rafah crossing complex between Gaza and Egypt, and the Israeli flag raised on the Gaza side.
Israeli Prime Minister Benjamin Netanyahu said seizing the crossing was a "very significant step" toward Israel's stated aim of destroying Hamas's military capabilities.
Residents reported heavy tank shelling on Tuesday evening in some areas of eastern Rafah. A Rafah municipal building caught fire after Israeli shelling, residents and Hamas media said.
Medics said one Palestinian was killed and several wounded in the building while an Israeli strike also killed two Palestinians on a motorcycle.
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.
A full-scale assault on Rafah would be a human catastrophe, the UN secretary-general says. (AP PHOTO)
"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.
"I am now seriously thinking of heading north, maybe to the central Gaza area. If they move further into Rafah, it will be the mother of massacres," he told Reuters via a chat app.
Many of those in Rafah were previously displaced from other parts of Gaza following Israel's orders to evacuate from there.
Families have been crammed into tented camps and makeshift shelters, suffering from shortages of food, water, medicine and other essentials.
The UN and other international aid agencies said the closing of the two crossings into southern Gaza - Rafah and Israeli-controlled Kerem Shalom - had virtually cut the enclave off from outside aid and very few stores were available inside.
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 UN aid agency UNRWA, said on X.
Separately, Jordan said Israeli settlers attacked a humanitarian convoy on its way to a crossing in northern Gaza.
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.
UN Secretary-General Antonio Guterres appealed to Israel and Hamas to spare no effort to get a truce deal.
"Make no mistake - a full-scale assault on Rafah would be a human catastrophe," he said.
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 to go to what it calls an "expanded humanitarian zone" some 20km away.
