Israel’s Prime Minister Benjamin Netanyahu said there would be no ceasefire in exchange for Hamas’ release of a US-Israeli hostage, who a source close to the group said could be freed Monday.

Hamas on Sunday said it would release Edan Alexander, a US-Israeli soldier held in Gaza, ahead of a visit by US President Donald Trump to the region, and as the group revealed it was engaged in direct talks with Washington towards a ceasefire.

No date was given, but a source close to Hamas told AFP 21-year-old Alexander would “most likely” be released on Monday or Tuesday.

“Most likely, Edan will be released today or tomorrow, Tuesday, but this requires securing field conditions,” the source said.

Hamas had demanded that American envoys ensure a “halt to all Israeli military operations... to create a safe corridor” for his transfer to the Red Cross, the source added.

The source said the Palestinian militant group had decided not to hold a public ceremony for the handover.

Netanyahu, meanwhile, said that “Israel has not committed to a ceasefire of any kind or the release of terrorists but only to a safe corridor that will allow for the release of Edan.”

Negotiations for a possible deal to secure the release of all hostages would continue “under fire, during preparations for an intensification of the fighting,” Netanyahu added.

Hamas had said Alexander would be released “as part of efforts towards a ceasefire” and the reopening of aid crossings.

Trump, who is due in Saudi Arabia on Tuesday, hailed the “monumental news” in a post on social media, describing it as a “good faith gesture.”

“Hopefully this is the first of those final steps necessary to end this brutal conflict,” he added.

Egypt and Qatar, who along with the US have mediated talks between Hamas and Israel, also welcomed the development, describing it in a joint statement as a “a gesture of goodwill and an encouraging step toward a return to the negotiating table.”

Earlier, two Hamas officials told AFP that talks were ongoing in Doha with the United States and reported “progress.”

Israeli strikes, meanwhile, continued, with Gaza’s civil defense agency reporting that at least 10 people were killed in an overnight Israeli airstrike on a school housing displaced people.

Of the 251 hostages seized during Hamas’ 7 October 2023 attack on Israel, 58 are still held in Gaza, including 34 the Israeli military says are dead.

Israel ended a two-month ceasefire on 18 March, launching a major offensive in Gaza and ramping up its bombardment of the territory.

It has also cut off all aid to Gaza, saying it would pressure Hamas to release the remaining hostages.

Washington had for decades publicly refused to engage directly with Hamas, which it labels a terrorist organization, before first doing so in March.

Hamas has continued to insist on a deal that ends the war and on 18 April rejected an Israeli proposal for a 45-day truce and hostage-prisoner exchange.

In its statement on Sunday, the group said it was willing to “immediately begin intensive negotiations” that could lead to an agreement to end the war and would see Gaza under a technocratic and independent administration.

Earlier this month, the Israeli government approved plans to expand its offensive in the Gaza Strip, with officials talking of retaining a long-term presence there.

While ceasefire negotiations have yet to produce a breakthrough, Israel’s foreign minister, Gideon Saar, on Sunday “fully” endorsed a US plan to restore aid to Gaza, under a complete blockade since 2 March.

The plan has drawn hefty international criticism for sidelining the United Nations and existing aid organizations, with the UN’s agency for Palestinian refugees, UNRWA, saying it was “impossible” to replace it in Gaza.

Hamas’ 2023 attack on southern Israel resulted in the deaths of 1,218 people, mostly civilians, according to an AFP tally based on official figures.

The health ministry in Hamas-run Gaza said on Sunday that at least 2,720 people have been killed since Israel resumed its campaign, bringing the overall death toll since the war broke out to 52,829.