US President Donald Trump on Sunday issued what he called his "last warning" to Hamas, urging the Palestinian militant group to accept a deal to release hostages from Gaza.

"The Israelis have accepted my Terms. It is time for Hamas to accept as well," Trump said in a post on his Truth Social platform.

"I have warned Hamas about the consequences of not accepting. This is my last warning, there will not be another one!"

Within hours of Trump's post, 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".

"The Hamas Movement welcomes any initiative that supports efforts to end the aggression against our people, and affirms its readiness to immediately sit at the negotiating table to discuss the release of all prisoners," the Palestinian militant group said.

Israel's N12 News had reported on Saturday that Trump has put forth a new ceasefire proposal to Hamas.

Under the deal, Hamas would free all the remaining 48 hostages on the first day of the truce in exchange for thousands of Palestinian prisoners jailed in Israel and negotiate an end to the war during a ceasefire in the enclave, according to N12.

An Israeli official said Israel was "seriously considering" Trump's proposal but did not elaborate on its details.

Meanwhile, Israel's army bombed a Gaza City residential tower on Sunday – the third in as many days – after Prime Minister Benjamin Netanyahu announced the military was "deepening" its assault on the Gaza Strip's key urban centre.

A day earlier, 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. (Agencies)