US President Donald Trump said in a social media post that Israel has agreed to an "initial withdrawal line" for Gaza, which has also been shared with Hamas.
Mr Trump said "when Hamas confirms," a ceasefire will be effective "immediately" and a prisoner exchange will begin, setting the stage for the next phase of Israel's withdrawal from the Palestinian enclave.
Israeli Prime Minister Benjamin Netanyahu said that he had instructed negotiators to travel to Egypt for talks over a Gaza deal.
Mr Netanyahu said that he hoped to bring home the hostages being held by Hamas in a matter of days.
Earlier, Mr Trump warned he would "not tolerate delay" from the Palestinian militant group, after it responded positively to his roadmap for freeing the captives and administering post-war Gaza.
While Mr Trump had called on Israel to halt its bombardment of Gaza following Hamas's announcement, the strikes continued on Saturday, with at least 57 people killed since dawn, according to the territory's civil defence agency.
Mr Netanyahu credited "military and diplomatic pressure" with compelling Hamas to agree to release the captives in a televised statement on Saturday.
"I hope that in the coming days we will be able to bring back all our hostages... during the Sukkot holidays," Mr Netanyahu said, referring to the Jewish festival that begins on Monday and runs for one week.
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The premier added he had ordered negotiators to Egypt "to finalise the technical details", with Cairo confirming it would also be hosting a delegation from Hamas for talks on "the ground conditions and details of the exchange of all Israeli detainees and Palestinian prisoners" as per Mr Trump's proposal.
Mr Trump also dispatched two envoys to Egypt on Saturday, according to the White House - his son-in-law Jared Kushner and his main Middle East negotiator Steve Witkoff.
Last night, Hamas announced "its approval for the release of all hostages - living and remains - according to the exchange formula included in President Trump's proposal".
Mr Trump immediately hailed the statement as evidence the group was "ready for a lasting PEACE", calling on Israel to stop its bombing.
He warned the group to "move quickly" towards a deal "or else all bets will be off".
Mr Netanyahu, meanwhile, insisted in his remarks that "Hamas will be disarmed... either diplomatically via Trump's plan or militarily by us".
A crowd of thousands has gathered in Tel Aviv urging Mr Trump to ensure a deal was struck.
Israeli strikes on Gaza kill 75
Despite Mr Trump's call for a pause in operations, Israel carried out deadly strikes across Gaza on Saturday.
"The death toll from the ongoing Israeli bombardment since dawn today stands at 57, including 40 in Gaza City alone," said Mahmud Bassal, a spokesman for the civil defence agency, a rescue organisation that operates under Hamas authority.
Israeli forces have carried out a sweeping air and ground assault in recent weeks around the city.
"The Israeli bombardment on Gaza continues with the same intensity and pattern - air strikes, artillery shelling and quadcopter drone fire are ongoing," said Mohammed al-Mughayyir, also of the civil defence agency.
Mahmud Al-Ghazi, 39, a resident of Al-Rimal neighbourhood in Gaza City, said "Israel has actually escalated its attacks" since Mr Trump's call for a pause.
"Who will stop Israel now? We need the negotiations to move faster to stop this genocide and the ongoing bloodshed," he added.
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The Israeli military said it was still operating in Gaza City and warned residents not to return there, adding that doing so would be "extremely dangerous".
Israeli media reported that the military had shifted to a defensive posture in Gaza following Mr Trump's call, though the military did not confirm this to AFP.
No role for Hamas
A Hamas official said Egypt, a mediator in the truce talks, would host a conference for Palestinian factions to decide on post-war plans for Gaza.
In its response to Mr Trump's plan, Hamas had insisted it should have a say in the territory's future.
The plan stipulates that Hamas and other factions "not have any role in the governance of Gaza", while also calling for a halt to hostilities, the release of hostages within 72 hours, a gradual Israeli withdrawal from Gaza and Hamas's disarmament.
Under it, administration of the territory would be taken up by a technocratic body overseen by a post-war transitional authority headed by Mr Trump himself.
Jamila al-Sayyid, 24, a resident of Gaza City's Al-Zeitoun neighbourhood, said he "was happy when Trump announced a ceasefire, but the warplanes did not stop".
An AFP journalist in the coastal area of Al-Mawasi reported hearing celebratory cries of "Allahu akbar!" (God is greatest) from tents housing Palestinians as news of Hamas's statement spread.
"The best thing is that President Trump himself announced a ceasefire, and Netanyahu will not be able to escape this time... (Trump) is the only one who can force Israel to comply and stop the war," said Sami Adas, 50, who lives in a tent in Gaza City with his family.
The war was triggered by Hamas's 7 October, 2023 attack on Israel, which resulted in the deaths of 1,219 people, mostly civilians, according to an AFP tally of Israeli official figures.
Israel's retaliatory offensive has killed at least 67,074 Palestinians, according to health ministry figures in the Hamas-run territory that the United Nations considers reliable.
Their data does not distinguish between civilians and combatants but indicates that more than half of the dead are women and children.
Meanwhile, Taoiseach Micheál Martin said the announcement by Hamas that it will release all remaining hostages, living and dead, will come as very welcome news to their families.
In a post on X, Mr Martin said that he hoped the move will open the way for an immediate ceasefire and the surging of aid into Gaza.
"There is an opportunity to now to create the lasting peace and I urge all parties to take it," he said.
The announcement by Hamas that it will release all remaining hostages, living and dead, will come as very welcome news to their families who have waited almost two years for their return.
— Micheál Martin (@MichealMartinTD) October 3, 2025
I hope it will open the way for an immediate ceasefire and the surging of aid into Gaza. pic.twitter.com/Ls1KooASzo
Tánaiste and Minister for Foreign Affairs Simon Harris welcomed the Hamas response that all remaining hostages will be released and called on Israel to stop the bombing and allow humanitarian aid into Gaza.
In a statement, he said: "There is also an opportunity to agree a path to a permanent peace and security for Israelis and Palestinians alike. Ireland steadfastly supports a Two State Solution."
Additional reporting Aisling Kenny, PA
