Hamas says it has received some ideas from the US through mediators on how to reach a Gaza ceasefire agreement.
The Palestinian armed group said it was discussing how to develop the ideas, noting that it was ready to release its 48 remaining hostages in Gaza in return for a clear declaration ending the war.
A Palestinian official told the BBC the US plan would see the hostages freed in the first 48 hours of a 60-day truce in exchange for Palestinian prisoners in Israeli jails and good-faith negotiations on a permanent ceasefire.
It came after US President Donald Trump gave Hamas what he called a last warning to agree a deal. He said Israel had accepted his terms, without giving details.
Israel's Foreign Minister, Gideon Saar, said it was ready to agree to a deal ending the war that would include the release of all the hostages - only 20 of whom are believed to be alive - and the disarmament of Hamas.
Prime Minister Benjamin Netanyahu meanwhile warned the approximately one million Palestinians living in famine-stricken Gaza City to evacuate immediately, as the Israeli military stepped up an offensive to conquer it.
Hospitals said Israeli attacks killed at least 40 people across Gaza on Monday, including 25 in Gaza City and elsewhere in the north.
The Israeli military said four soldiers were killed in combat in northern Gaza.
On Sunday evening, Hamas put out a statement saying it had received through the mediators some ideas from the American side aimed at reaching a ceasefire agreement and welcomed the initiative.
Hamas said it was ready to immediately negotiate the release of all those taken hostage during the group's attack on Israel on 7 October 2023, in exchange for an end to the war, a full withdrawal from Gaza, and the formation of a committee of Palestinian independents to manage Gaza.
Earlier in the day, President Trump had written on Truth Social: Everyone wants the Hostages HOME. Everyone wants this War to end! The Israelis have accepted my Terms. It is time for Hamas to accept as well.
A senior Palestinian official familiar with the ceasefire efforts stated that under the US proposal, all hostages would be released within the first 48 hours of a proposed truce, in exchange for Palestinian prisoners, including those serving lengthy sentences, and detainees from Gaza.
During the initial two weeks of the truce, negotiations would cover critical issues, including Hamas's disarmament and arrangements for Israeli troop withdrawals.
Israeli media reported that the government was seriously considering the US plan, while concerns remained about Hamas's acceptance.
Israeli Minister Saar emphasized that Israel was prepared to accept a full deal to end the conflict based on the cabinet's decision, emphasizing the need for the return of hostages and disarmament of Hamas.
The Israeli military has intensified its air and ground attacks on Gaza City, claiming ongoing operations in response to the humanitarian crisis and military aggression from Hamas.
The UN has issued warnings regarding the deteriorating humanitarian conditions in Gaza, as overcrowding and safety issues plague tent camps throughout the region.
The conflict began following Hamas's attacks on 7 October 2023, which resulted in significant casualties and ongoing military actions from Israel.
