By Nidal al-Mughrabi and Samia Nakhoul

CAIRO (Reuters) -Hamas will release the Israeli-American hostage Edan Alexander held in Gaza, a senior Hamas official told Reuters on Sunday.

Freeing Alexander, believed to be the last surviving American hostage held by the militant Palestinian group, comes ahead of U.S. President Trump's visit to the Middle East this week.

A source familiar with the matter said Alexander would likely be released on Tuesday.

It is part of efforts to reach a ceasefire agreement and allow humanitarian aid to enter the besieged enclave, the Palestinian militant group said.

Another official, the exiled Gaza Hamas chief Khalil al-Hayya, said efforts to facilitate the release have been jointly carried out by Qatar, Egypt, and Turkey.

"The movement affirms its readiness to immediately start intensive negotiations and make serious efforts to reach a final agreement to end the war, exchange prisoners in an agreed-upon manner," Hayya added.

Direct four-way talks that led to the release were held between officials from the U.S., Qatar, Egypt and Hamas, a source briefed on the negotiations told Reuters.

There was no immediate comment from the Israeli prime minister's office on the announcement.

Hamas had released 38 hostages under a ceasefire that began on January 19. In March, Israel's military resumed its ground and aerial offensive on Gaza, abandoning the ceasefire after Hamas rejected proposals to extend the truce without ending the war.

Israeli officials said that offensive will continue until the remaining 59 hostages are freed and Gaza is demilitarized. Hamas insists it will free hostages only as part of a deal to end the war and has rejected demands to lay down its arms.

Hamas has said it is willing to free all remaining hostages its gunmen seized in attacks in southern Israel on October 7, 2023, and to agree to a permanent ceasefire if Israel pulls out completely from Gaza.

Israel, which is in control of around a third of Gaza's territory and has been imposing an aid blockade since March, said in May it will expand its Gaza offensive.

U.S. special envoy Adam Boehler said: “It’s a positive step forward and we would also ask that Hamas release the bodies of four other Americans that were taken."

A State Department spokesperson said Hamas bore sole responsibility for the war as well as for the resumption of hostilities.

The U.S. had previously held discussions with the Palestinian militant group on securing the release of U.S. hostages held in Gaza.

Israeli media reported on Sunday that Prime Minister Benjamin Netanyahu had told a closed session of the Foreign Affairs and Defense Committee that Hamas could soon release Alexander, an American-Israeli hostage, as a goodwill gesture towards Trump, who will visit the Middle East this week.

The prime minister's office did not immediately respond to a request for comment on the reports.

Israel launched its campaign in Gaza in retaliation for the Hamas attack on October 7, 2023 that killed 1,200 people, according to Israeli tallies, and saw 251 taken hostage into Gaza in the deadliest day for Israel in its history.

The campaign has killed more than 52,800 Palestinians, according to local health authorities, and has devastated the Gaza Strip, leaving its 2.3 million population depending on aid supplies that have been dwindling rapidly since the blockade.

(Reporting by Samia Nakhoul and Nidal al-Mughrabi ; Editing by Leslie Adler and David Gregorio)