"I hope, for the good of the Middle East, that Hamas takes this Deal, because it will not get better — It will only get worse" Trump said.
The news comes as Trump prepares to host Israeli Prime Minister Benjamin Netanyahu for talks at the White House on Monday. The U.S. president has shown increased interest in a ceasefire and hostage agreement in the region after the U.S. brokered a peace agreement between Israel and Iran.
But Hamas' response, which emphasized its demand that the war end, raised questions about whether the latest offer could materialize into an actual pause in fighting.
Hamas official Taher al-Nunu said the militant group was "ready and serious regarding reaching an agreement."
He said Hamas was "ready to accept any initiative that clearly leads to the complete end to the war."
A Hamas delegation is expected to meet with Egyptian and Qatari mediators in Cairo on Wednesday to discuss the proposal, according to an Egyptian official. The official spoke on condition of anonymity because he wasn't authorized to discuss the talks with the media.
Throughout the nearly 21-month-long war, ceasefire talks between Israel and Hamas have repeatedly faltered over whether the war should end as part of any deal.
Hamas has said it is willing to free the remaining 50 hostages, less then half of whom are said to be alive, in exchange for a complete Israeli withdrawal from Gaza and an end to the war.