The Hamas terrorist group said Friday it has issued a "positive response" to a U.S.-mediated ceasefire proposal in its war with Israel.

In a post to Telegram, Hamas said it "submitted a positive response to the mediators' latest proposal."

It added that it was "fully prepared to immediately enter into a round of negotiations on the mechanism for implementing this framework," according to a translation of the post. 

On Tuesday, President Trump announced that Israel had agreed to a proposal for a two-month ceasefire. At the time, neither Israel nor Hamas confirmed Mr. Trump's statement. 

"I think it's been very positive, a good response," Mr. Trump told reporters late Friday night aboard Air Force One regarding the Hamas statement. 

"There could be a Gaza deal next week," the president later added. "...I'm very optimistic, but you know, it changes from day to day. It's been changing for years."

Israeli sources told CBS News on Wednesday that while there was support for the terms of the proposal by Israeli Prime Minister Benjamin Netanyahu's cabinet, Israel was not committing to it yet. 

Netanyahu is expected to visit Washington, D.C., on Monday to meet with Mr. Trump at the White House. 

A Palestinian official told The Associated Press on Friday that Hamas was still working on its response to the proposal presented to it by Egyptian and Qatari mediators. He said Hamas is insisting on guarantees regarding an Israeli withdrawal to positions it held on March 2, during a previous ceasefire, and an end to the war following a 60-day truce, as well as ending the U.S. and Israeli-backed Gaza Humanitarian Foundation (GHF) system for distributing aid. The official spoke on the condition of anonymity because he was not authorized to talk to the media.

The Hamas-run Gaza Health Ministry says the number of Palestinians killed in the territory has passed 57,000 since the war began about 21 months ago. The ministry does not differentiate between civilians and combatants in its count, but says more than half of the dead are women and children.

The war began when Hamas-led militants attacked southern Israel on Oct. 7, 2023, killing about 1,200 people and taking roughly 250 hostages.

Meanwhile, the Gaza Health Ministry says at least 640 civilians have been shot to death in recent weeks trying to access desperately needed humanitarian supplies, including more than 400 at distribution sites run by GHF. 

Since it began operating in Gaza on May 26, GHF has faced near-daily claims of aid-seekers being killed by Israeli forces as they try to reach its four hubs in Gaza. 

"I do not want to diminish these reports, but we can't control what happens outside our distribution sites," GHF's director, American evangelical reverend Johnnie Moore, told CBS News in an interview Tuesday in response to a question about reports from doctors and eyewitnesses that Israeli soldiers have repeatedly opened fire on unarmed civilians trying to reach its aid hubs.

Earlier this week, more than 170 humanitarian groups called for the opaquely run organization — which has never revealed its funding or management structure — to be disbanded and all aid efforts in Gaza to be reorganized under the long-established United Nations-led system. Those international humanitarian efforts have been largely blocked by Israel since March.