Israeli forces hammered Rafah in southern Gaza with tanks and artillery Saturday, hours after US President Joe Biden said Israel was offering a new roadmap towards a full ceasefire.
Shortly after Biden's announcement, Israeli Prime Minister Benjamin Netanyahu insisted his country would still pursue the war until it had reached all its aims.
He reiterated that position on Saturday, saying that "Israel's conditions for ending the war have not changed: the destruction of Hamas's military and governing capabilities, the freeing of all hostages and ensuring that Gaza no longer poses a threat to Israel".
Hamas, meanwhile, said it "views positively" the Israeli plan laid out by Biden.
In his first major address outlining a possible end to the nearly eight-month war, the US president said Israel's three-stage offer would begin with a six-week phase that would see Israeli forces withdraw from all populated areas of Gaza.
It would also see the "release of a number of hostages... in exchange for (the) release of hundreds of Palestinian prisoners".
Israel and the Palestinians would then negotiate for a lasting ceasefire -- but the truce would continue so long as talks are ongoing, Biden said.
The US leader urged Hamas to accept the Israeli proposal, even though it was Israel rejected an almost identical offer mediated by Egypt and Qatar, and accepted by Hamas, last month.
"It's time for this war to end, for the day after to begin," he said.
US Secretary of State Antony Blinken called his counterparts from Jordan, Saudi Arabia and Turkey on Friday to press the deal.
UN chief Antonio Guterres "strongly hopes" the latest development "will lead to an agreement by the parties for lasting peace", his spokesman Stephane Dujarric said.
German Foreign Minister Annalena Baerbock said the offer "provides a glimpse of hope and a possible path out of the war's deadlock", while EU chief Ursula von der Leyen welcomed a "balanced and realistic" approach to end the bloodshed.
Saudi Arabia stressed its "support for all efforts aimed at an immediate ceasefire" and the withdrawal of Israeli troops.
Indonesia, meanwhile, said it was ready to send "significant peacekeeping forces" and medical personnel to Gaza if a ceasefire is agreed.
But Netanyahu took issue with Biden's presentation of what was on the table, insisting on Friday the transition from one stage to the next was "conditional" and crafted to allow Israel to maintain its war aims.
"The prime minister authorised the negotiating team to present an outline for achieving (the return of hostages), while insisting that the war will not end until all of its goals are achieved," Netanyahu's office said.
"The exact outline proposed by Israel, including the conditional transition from stage to stage, allows Israel to maintain these principles."
Israel has repeatedly vowed to destroy Hamas since the Palestinian militant group attacked southern Israel on October 7.
Israeli opposition leader Yair Lapid said the government "cannot ignore Biden's important speech" and should accept the proposed deal, vowing to back Netanyahu if his far-right coalition partners quit over it.
"I remind Netanyahu that he has our safety net for a hostage deal," Lapid said Saturday on social media platform X.
Israel sent tanks and troops into Rafah in early May, ignoring concerns over the safety of displaced Palestinian civilians sheltering in the city on the Egyptian border.
On Saturday, residents reported tank fire in the Tal al-Sultan neighbourhood in west Rafah, while witnesses in the east and centre of Rafah described intense shelling.
"From the early hours of the night until this morning, the aerial and artillery bombardment has not stopped for a single moment", a resident from west Rafah told AFP on condition of anonymity.
"There are a number of occupation (Israeli) snipers in high-rise buildings overseeing all areas of Tal al-Sultan... making the situation very dangerous", the resident added.
There was also shelling and gunfire from the Israeli army in Gaza City, in the north of the territory, an AFP reporter said.
Before the Rafah offensive began, the United Nations said up to 1.4 million people were sheltering in the city.
Since then, one million have fled the area, the UN agency for Palestinian refugees, UNRWA, has said.
The Israeli seizure of the Rafah crossing has further slowed sporadic deliveries of aid for Gaza's 2.4 million people and effectively shuttered the territory's main exit point.
Israel said last week that aid deliveries had been stepped up.
But Blinken acknowledged on Friday that the humanitarian situation was "dire" despite US efforts to bring in more assistance.
Egyptian state-linked Al-Qahera News said Cairo will host a meeting with Israeli and US officials on Sunday to discuss the reopening of the Rafah crossing.
The World Food Programme said daily life had become "apocalyptic" in parts of southern Gaza.
Israel's offensive has killed at least 36,379 people in Gaza, mostly civilians.
In northern Gaza, witnesses said that after carrying out a three-week operation in the town of Jabalia and its neighbouring refugee camp, troops had ordered residents of nearby Beit Hanun to evacuate ahead of an imminent assault.
The Israeli army said troops "completed their mission in eastern Jabalia and began preparation for continued operations in the Gaza Strip".
Jabalia shopkeeper Belal al-Kahlot said there was nothing left of his store after the Israeli operation.
"Everything is ashes," he told AFP.