Israel's Cabinet has approved a deal that would allow for the release of at least 50 hostages over the course of a four-day pause in hostilities, Israel's Prime Minister said early Wednesday morning. As a part of this deal, 150 Palestinian prisoners will also be released by Israel.

Prime Minister Benjamin Netanyahu said in a release the “Israeli government has approved the outline to the first phase” of bringing hostages home, with at least 50 being released over the course of the four-day pause in fighting.

The Government of Israel, the IDF and the Israeli security forces will continue to fight the war for the return of all hostages, the elimination of Hamas and to ensure that Gaza will not pose a threat to Israel, according to Netanyahu.

Earlier, sources told ABC News 42 hostages would be released.

A short while later, Hamas released its own statement early Wednesday morning local time, which had some of the same terms announced by Prime Minister Benjamin Netanyahu.

Hamas confirmed via Telegram a temporary cease-fire of four days, with the release of 50 women and children who’ve been held hostage.

In exchange, Hamas said Israel agreed to release 150 Palestinian women and children. Hamas said the juveniles released would be under 19 years old.

The U.S. expects that Abigail Edan, an orphaned 3-year-old Israeli-American who was kidnapped by Hamas militants on Oct. 7, would be among the hostages released as part of any initial deal between Israel and Hamas, according to a U.S. official familiar with negotiations. However, the Biden administration hasn’t received any reliable guarantee that she or any of the missing Americans will be freed in the arrangement, the official said.

The official said there are many significant concerns surrounding the hostages' passage out of Gaza, and that moving the hostages out of the enclave as quickly as possible would be necessary for their protection and to facilitate ongoing talks.

While American negotiators are currently zeroed-in on securing an initial deal -- rather than focusing on subsequent swaps that might happen in exchange for a longer pause -- Hamas is expected to provide information about the conditions of hostages that will remain in custody, which could be critical in shaping the strategy going forward, the official said.

-ABC News' Shannon Crawford

Israeli Prime Minister Benjamin Netanyahu, speaking ahead of Tuesday's cabinet meeting and vote on a potential hostage deal, said Israel's war against Hamas will not stop after a cease-fire.

Netanyahu said the war will continue until Hamas is destroyed, all hostages are brought home and Israel has ensured "that there will be no element in Gaza that threatens Israel."

Israeli Defense Minister Yoav Gallant added that without the continuation of Israel's operations in Gaza, there'd be no chance of bringing home more hostages.

-ABC News' Will Gretsky

National Security Council spokesman John Kirby remained tightlipped on the possible hostage deal, telling reporters Tuesday, "We're all hopeful, but we won't say and do not want to say, anything in these delicate hours that could put a deal at greater risk."

If a deal is reached, Kirby said the first step would be to secure safe passage for the hostages into Israel, where many would likely need immediate medical attention before they return to their home countries.

Pressed by ABC News about how long it could take for the safe passage to be secured and hostages released after a deal is reached, Kirby said, "Depending on if we get a deal, depending on how many hostages are arranged for, depending on where they are, depending on their physical condition and their mobility, I think we all need to be humble in terms of the appropriate amount of time it could take to physically move them to safety."

"Some of these people could be in pretty rough shape. I think we all need to be prepared for the fact that it could take hours, if not days, to complete their release," he said.

-ABC News' Molly Nagle

Hamas announced that it will be delaying the release of Israeli hostages, accusing Israel of violating the cease-fire agreement regarding aid trucks and the agreed-upon terms for the release of Palestinians imprisoned in Israel.

The Al-Qassam Brigades -- the armed wing of Hamas -- said it had decided to delay Saturday's scheduled second round of hostage releases until Israel committed to allowing aid trucks to enter northern Gaza. Hamas was expected to release 13 Israeli hostages in exchange for the release of 39 Palestinians imprisoned in Israel on Saturday, sources told ABC News.

"The Al-Qassam Brigades decides to delay the release of the second batch of hostages until the occupation adheres to the terms of the agreement regarding the entry of relief trucks into the northern Gaza Strip, and due to its failure to adhere to the agreed-upon criteria for releasing prisoners," Al-Qassam Brigades said in a statement.

Hamas leader Osama Hamdan, who is based in Lebanon, said relief trucks that arrived in northern Gaza today were half of the number that was agreed upon.

"There are violations committed by the Israelis in implementing the terms of the truce, some of which occurred yesterday and were repeated today," Hamdan said Saturday, adding that another issue at stake was the reported shooting of two Palestinians on Friday as they tried to reach northern Gaza.

A senior Israeli political source told ABC News that Israel did not violate the agreement. The IDF said about 200 trucks carrying humanitarian aid are expected to enter Gaza today, after 200 trucks with aid entered Gaza yesterday via the Rafah crossing and delivered their cargo to international aid organizations.

The Palestinian Red Crescent said 61 trucks carrying food, water and medical supplies headed to northern Gaza on Saturday, the largest aid convoy to reach the area since the start of the war.

-ABC News' Ayat Al-Tawy, Nasser Atta, Jordana Miller