In a copy of the statement seen by Reuters, Hamas issued its response to Trump's 20-point plan after the US president gave the Palestinian militant group until Sunday to accept or reject the proposal.
Trump has not said whether the terms would be subject to negotiation, as Hamas is seeking.
Notably, Hamas did not say whether it would agree to a stipulation that it disarm, a demand by Israel and the US that it has previously rejected.
In its statement, Hamas said it "appreciates the Arab, Islamic, and international efforts, as well as the efforts of US President Donald Trump, calling for an end to the war on the Gaza Strip, the exchange of prisoners, (and) the immediate entry of aid," among other terms.
It said it was announcing its "approval of releasing all occupation prisoners - both living and remains - according to the exchange formula contained in President Trump's proposal, with the necessary field conditions for implementing the exchange".
But Hamas added: "In this context, the movement affirms its readiness to immediately enter, through the mediators, into negotiations to discuss the details."
The group said it was ready "to hand over the administration of the Gaza Strip to a Palestinian body of independents (technocrats) based on Palestinian national consensus and supported by Arab and Islamic backing."
The White House did not immediately respond to a request for comment on Hamas' response to the proposal, which is backed by Israel as well as Arab and European powers.
Trump's plan specifies an immediate ceasefire, an exchange of all hostages held by Hamas for Palestinian prisoners held by Israel, a staged Israeli withdrawal from the Gaza Strip, the disarmament of Hamas and the introduction of a transitional government led by an international body.
Trump had earlier on Friday urged Hamas to accept the proposal to end the nearly two-year-old war or else "all hell" would break out.
"An agreement must be reached with Hamas by Sunday Evening at SIX (6) PM, Washington, DC time," Trump posted on social media on Friday.
"Every Country has signed on! If this LAST CHANCE agreement is not reached, all HELL, like no one has ever seen before, will break out against Hamas."
Trump first presented his plan to leaders and officials from Egypt, Indonesia, Jordan, Saudi Arabia, Turkey, Pakistan, Qatar and the United Arab Emirates on the sidelines of last week's United Nations General Assembly.
Mediators Qatar and Egypt then shared the 20-point plan with Hamas late on Monday after Israeli Prime Minister Benjamin Netanyahu appeared alongside Trump at the White House and endorsed the document, saying it satisfied Israel's war aims.
In his Truth Social post on Friday, Trump made an apparent reference to Israel's offensive in Gaza City.
He said remaining Hamas militants in the city are trapped and "will be hunted down, and killed" without a deal, and warned "innocent Palestinians" to leave for safer areas of the Gaza Strip.
The UN has repeatedly said that nowhere in the strip is safe.
Surviving Hamas fighters would be allowed to leave under the proposal, Trump said in his message.
"This deal also spares the lives of all remaining Hamas fighters!" his Truth Social post said.
Israel blocked Gaza City's main road on Thursday and has told its million residents to flee south, warning it was their last chance to escape a major offensive.
"President Trump's Gaza initiative opens a window of opportunity. It offers both a chance for Palestinians to receive life-saving aid at the scale urgently needed, and to bring the hostages home," UN aid chief Tom Fletcher said in a statement on Friday.
"We are ready and eager to act."
Israel began its offensive in the Gaza Strip after the October 7, 2023 Hamas-led attack on Israel in which 1200 people were killed and 251 taken as hostages back to the enclave, according to Israeli tallies.
Israel's military campaign has killed more than 66,000 people in the strip, most of them civilians, according to Gaza health authorities.
with AP
