"The Israelis have accepted my terms. It is time for Hamas to accept as well. I have warned Hamas about the consequences of not accepting. This is my last warning," Trump said on social media, without elaborating further. 

In a statement released shortly after, Hamas said it was ready to "immediately sit at the negotiating table" following what it described as "some ideas from the American side aimed at reaching a ceasefire agreement."

US news outlet Axios reported that White House envoy Steve Witkoff sent a new proposal for a Gaza hostage and ceasefire deal to Hamas last week.

The White House has not released any details about the proposal but late Sunday Trump said "you'll be hearing about it pretty soon," as he portrayed the negotiations in a positive light.

"We had some very good discussions. Good things could happen," he told reporters. "I think we're going to have a deal on Gaza very soon."

In early March, Trump issued a similar ultimatum to Hamas, demanding it free all remaining hostages immediately and turn over bodies of dead hostages, saying if not, "it is OVER for you."

Israeli campaign group the Hostages and Missing Families Forum welcomed the US president's latest intervention as a "true breakthrough."

Hamas militants seized 251 hostages during the massive October 7, 2023 attack on Israel, with 47 still believed to be in Gaza.

The Israeli military says 25 of them are dead. Israel is seeking the return of their remains.

The statements from Trump and Hamas came as Israel's army bombed a Gaza City residential tower Sunday -- the third in as many days -- after Prime Minister Benjamin Netanyahu announced the military was "deepening" its assault on the key urban center.

Witness Mohammed Al-Nazli told AFP that the strike on the Al-Roya tower "felt like an earthquake."

At least 48 people were killed in Sunday's Israeli attacks, according to Gaza civil defense agency spokesman Mahmud Bassal.

The air force has leveled two other residential high-rises under the same claim that Hamas had used them as observation points.

Netanyahu said on Sunday that around 100,000 residents had already left Gaza City, accusing Hamas of trying to prevent evacuations and of using civilians as "human shields."

The escalation has fueled fears of a further deterioration in already dire humanitarian conditions for Palestinians living in the area.

On Saturday, Israeli protesters took to the streets to call on their government to reverse the decision to seize Gaza City, fearing for the fate of hostages believed to be held there.

The October 7, 2023 attack resulted in the deaths of 1,219 people, mostly civilians, according to an AFP tally based on Israeli figures.

Israel's retaliatory offensive has killed at least 64,368 Palestinians, most of them civilians, according to figures from the health ministry in Hamas-run Gaza that the United Nations considers reliable.

Media restrictions in Gaza and difficulties in accessing many areas mean AFP is unable to independently verify the tolls and details provided by the civil defense agency or the Israeli military.