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(LONDON and TEL AVIV) -- Israeli Prime Minister Benjamin Netanyahu will convene his cabinet to discuss the proposed Gaza Strip ceasefire deal on Thursday, with the cabinet and the wider government expected to approve the blueprint to end the two-year-old war.

The cabinet will meet after days of intense negotiations in the Egyptian Red Sea city of Sharm el-Sheikh, where Israeli and Hamas representatives hashed out the final details of a plan based on the 20-point proposal presented by U.S. President Donald Trump last month.

Family members of some of the hostages said they are "encouraged" by the overnight developments, but remain in a "state of cautious optimism."

"We have to keep the eyes on the ball to make sure this deal is fully consummated and nobody screwed up," Rotem Cooper, whose son, Amiram Cooper, is being held hostage, said in a video statement on Thursday.

Cooper added that this is "an historic day" in Israel.

"We're still processing it, we still can't believe it, but it's happening, and we need to make sure it's gonna happen,” Cooper said.

Netanyahu had been expected to convene his cabinet meeting at 5 p.m. local time, 10 a.m. ET. But that meeting has now been delayed to 1 p.m. ET, with a vote expected to occur around 2 p.m. ET. The cabinet is expected to approve the deal, after which the proposal will be put to the wider government to ratify.

The cessation of all fighting by the IDF and Hamas will go into effect after the Israel government ratifies the deal, according to an Israeli official.

Trump announced on Wednesday that Israel and Hamas had agreed to the first phase of the deal, in which all remaining hostages -- alive and dead -- will be released from Gaza in exchange for an as-yet undetermined number of Palestinians being held in Israeli prisons. Nearly 2,000 prisoners are believed to be under discussion for release.

The Israel Defense Forces will also pull back to the so-called "yellow line" in Gaza -- a reference to a proposed ceasefire map released by the White House last month showing multiple stages of withdrawal. The full details of the agreed-to deal have not been made public and the exact location of that "line" may have shifted during the negotiations.

A senior Israeli official told ABC News that the 72-hour window for Hamas releasing all hostages will begin after the Israeli government ratifies the deal, which it is expected to do on Thursday.

The 20 hostages thought to still be alive are therefore expected to be released all in one group, the official said.

During a meeting with his Cabinet on Thursday afternoon, Trump said he expects the hostages to be released on Monday or Tuesday.

"Getting them is a complicated process. I'd rather not tell you what they have to do to get them," Trump told his Cabinet members. "They're in places you don't want to be. But we are getting the hostages back on Monday or Tuesday, and that will be a day of joy."

The president said that in addition to those hostages still alive, he expects Hamas to also turn over the remains of 28 people who died while being held hostage, "mostly young, mostly men and boys."

"To those parents, the dead young man is just as important as the person alive," Trump said.

Trump said he is planning to travel to the Middle East, but is still working on the timing.

"We're going to go to Egypt, where we'll have a signing, an additional signing," Trump said, referring to the proposed ceasefire agreement. "We've already had a signing representing me, but we're going to have an official signing."

The president thanked members of his Cabinet, whom he said were instrumental in the negotiations, specifically Secretary of State Marco Rubio; the administration's Middle East envoy, Steve Witkoff; and Secretary of Defense Pete Hegseth.

He also thanked all of the countries in the Middle East, including Egypt, Qatar, Saudi Arabia and the United Arab Emirates, for their work in forging the proposed ceasefire deal.

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