Hamas approved a 60-day ceasefire proposal with Israel which included the return of half of the hostages held in Gaza and the release of a number of Palestinian prisoners by Israel.
Hamas senior official Basem Naim confirmed the group's approval. Hamas said other Palestinian factions had also notified mediators of their approval.
There was no Israeli response to Hamas' own proposal, but an Israeli official confirmed the proposal had been accepted.
Egypt and Qatar mediated between the two sides with US support.
Israel's plans to control Gaza City at the heart of the Palestinian territories have raised concerns abroad and at home.
Tens of thousands of Israelis on Sunday staged the biggest demonstration since the war began. They urged an agreement to end the fighting and release the remaining 50 hostages detained in Gaza since the Hamas attack on October 7, 2023.
While Israeli officials believe 20 people are still alive.
Thousands of Palestinians concerned about an imminent Israeli ground attack are leaving their homes in the eastern region of Gaza City, which is now under the ongoing Israeli bombing, towards points in the west and south in the devastated region.
In a apparent show of strength on Monday, Israeli tanks moved forward to the outskirts of Sabra in Gaza City, according to witnesses who calculated the presence of at least nine tanks and bulldozers.
Israel's Army Chief of Staff, Lieutenant General Eyal Zamir, said his country was at a turning point in the Gaza war, "with a focus on increasing attacks on Hamas in Gaza City," the military spokesman said in a statement.
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In a video released by his office, Prime Minister Benjamin Netanyahu said: "I, like you, hear reports in the media, and from there you can get one impression - Hamas is under enormous pressure."
An official Egyptian source stated that the proposal received by Hamas included a 60-day suspension of Israeli military operations and outlined a framework for a comprehensive deal to end the conflict that has lasted nearly two years.
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