Israel-Gaza updates: Israel says ground operation underway in southern Gaza

The Israeli Prime Minister's Office announced Monday afternoon that negotiations with Hamas "on the list of those slated to be released under the framework of the hostages release outline are continuing."

"We are aware of the tension in the families and will release additional information when possible," the office said in a statement. "We request to refrain from disseminating rumours and unreliable information."

A fourth prisoner swap between the warring sides was expected to take place Monday between 4 and 6 p.m. local time on the final day of the agreed upon cease-fire, which is set to expire Tuesday at 7 a.m. local time.

-ABC News' Dana Savir and Morgan Winsor

U.S. National Security Council spokesperson John Kirby said Monday that an estimated seven to 10 American hostages remain in the war-torn Gaza Strip.

"We know that there are other Americans being held hostage. We're certainly going to do everything we can hour by hour to get them released," Kirby told ABC News' George Stephanopoulos in an interview on "Good Morning America."

"We know that there were 10 unaccounted for, missing Americans," he added. "We think that the large majority of them are in this hostage population. But we don't have great fidelity past that."

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John Kirby talks possible release of more American hostages in Gaza cease-fire

The National Security Council spokesperson discusses where things stand as far as more hostages being released before the cease-fire runs out.

ABCNews.com

Kirby noted that it’s also "difficult to know" exactly how many total hostages are in Gaza and which groups are currently holding them.

"We have to assume there are a couple hundred or so," he said. "We also have to assume, George, that Hamas isn't holding all of them -- that the other groups, potentially the Palestinian Islamic Jihad, for instance, another radical extremist terrorist group there operating out of Gaza, could be holding some. But it's going to be up to Hamas now to track all them down and see if we can arrange for their exchange."

With a four-day cease-fire between Gaza's militant rulers, Hamas, and Israel set to expire Tuesday morning, a fourth and final prisoner swap is expected to take place Monday between 4 and 6 p.m. local time, according to Israeli authorities.

"We're into day four now and so our hope and expectation is yet another instalment of hostages will get released sometime later today," Kirby told ABC News. "There have been delays in the past couple of days. We'll see if we have to work through any delays today."

"We would very much like to see this pause continue and more hostages exchanged as a result," he continued. "Isreal has said they're willing to do that. It's really going to be up to Hamas now to determine whether they're willing to come up with more hostages in coming days."

-ABC News' Morgan Winsor

Discussions are being held on a list that was received overnight regarding the final group of hostages who are expected to be released by Hamas in the Gaza Strip on Monday, according to the Israeli Prime Minister’s Office.

The office said in a statement on Monday morning that the list "is now being evaluated in Israel" and "additional information will be issued when possible."

Sources told ABC News that there are "problems" with the current list for Monday.

Monday's prisoner swap between Hamas and Israel -- the fourth round amid a four-day cease-fire -- is expected to take place between 4 and 6 p.m. local time.

-ABC News' Jordana Miller, Dana Savir and Morgan Winsor

Israel’s President Isaac Herzog is set to meet with Elon Musk on Monday afternoon, his office said Sunday.

"Against the background of the ongoing war with Hamas, President Isaac Herzog will tomorrow (Monday), meet with businessman Elon Musk, who is visiting Israel," the president's office said in a statement Sunday evening.

"[R]epresentatives of the families of hostages held by Hamas, who will speak about the horrors of the Hamas terror attack on October 7, and of the ongoing pain and uncertainty for those held captive," the statement continued. "In their meeting, the President will emphasize the need to act to combat rising antisemitism online."

The meeting will be closed to the media.

The Tesla boss also owns social media platform X, formerly Twitter.

-ABC News’ Jordana Miller