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

Three doctors were killed in a strike at northern Gaza's Al-Awda Hospital, according to Doctors Without Borders.

The hospital said only medical personnel, patients and the injured were inside the facility at the time.

Hospital officials called on the international community to provide a safe corridor for the evacuation of patients and medical staff.

"We mourn the loss of our colleagues," Doctors Without Borders said in a statement. "We condemn this strike in the strongest terms, and call yet again for the respect and protection of medical facilities, staff and patients. We reiterate our call for an immediate cease-fire to prevent more deaths in Gaza."

The first group of Israeli hostages have been released by Hamas in the Gaza Strip and handed over to the International Committee of the Red Cross, two sources briefed on the matter told ABC News.

The sources said the Red Cross has the hostages and that the "operation" to get them home has begun.

It was expected that 13 Israeli hostages would be freed by Hamas near Gaza's border with Egypt on Friday in a prisoner exchange deal. But it was unclear exactly how many were handed over to the Red Cross.

-ABC News' Matt Gutman and Morgan Winsor