Israel-Gaza live updates: 'Constructive meeting' but 'gaps' remain: Israeli PM

The White House does not support Israel’s plan to build "buffer zones" inside Gaza and along the border with Israel, National Security Council spokesperson John Kirby said.

"We do not want to see the territory of Gaza reduced in any way. We won't support that," Kirby said.

Asked if U.S. officials have told Israel that they don’t support creating these buffer zones, Kirby said they’ve consistently shared their beliefs.

"I won’t talk about our diplomatic conversations. We have been very clear and consistent, both in private and publicly, that we do not want to see the territory of Gaza reduced in any way," Kirby said.

Kirby was also asked if the U.S. supports negotiations that CNN has reported, describing a deal where Hamas leaders can leave Gaza in exchange for a cease-fire.

"We don't want to see Hamas in charge of Gaza anymore. They chose to violate the cease-fire that was in place, and we certainly agree with our Israeli counterparts that whatever the future of post-conflict Gaza looks like, it can’t include Hamas leaders. Now, how that's actualized, I think I'd refer to the Israeli Defense Forces to speak to," he said, declining to get ahead of discussions underway.

"The last thing I'll say on this is we have been very consistent, that whatever governance looks like in Gaza, after this is over, it's got to be representative of the aspirations of the Palestinian people who are not represented by Hamas, and who do not, [in] majority, don't support what Hamas has put them through in visiting this kind of violence inside the strip," Kirby said.

-ABC News’ Cheyenne Haslett

The Israel Defense Forces said Tuesday that 21 of its reservists were killed "during operational activity" in the central Gaza Strip a day earlier.

An "RPG missile was apparently fired by terrorists" at an Israeli tank that was securing an area near the Gaza-Israel border where Israeli troops were rigging buildings with explosives for demolition, according to IDF spokesperson Rear Adm. Daniel Hagari.

"At the same time, an explosion occurred in two two-storey buildings, which collapsed as a result, while most of the force was inside and near them," Hagari said in a statement Tuesday. "The buildings apparently exploded as a result of mines that our forces planted in them and were about to explode the buildings, the terrorist infrastructure in the area."

The IDF is "investigating the details of the incident and the cause of the explosion," according to Hagari.

"War has a very painful and heavy price," he added. "The dedicated reservists, who stood up for the flag, sacrificed the most precious of all, for the security of the State of Israel and so that we can all live here safely."

Three more Israeli soldiers were killed in a separate incident in the southern Gaza city of Khan Younis on Monday, bringing the toll to 24, according to the IDF. It was the deadliest day for the Israeli military since the war with Hamas began on Oct. 7.

Israeli Prime Minister Benjamin Netanyahu called it "one of the hardest days since the war broke out."

"We must learn the necessary lessons and do everything to safeguard the lives of our fighters." Netanyahu said in a statement Tuesday. "On behalf of our heroes, for our very lives, we will not stop fighting until total victory."

"Our hearts are with the dear families in their most difficult time," Israeli Defense Minister Yoav Gallant said.

He added, "This is a war that will determine the future of Israel for decades to come -- the fall of the fighters is a requirement to achieve the goals of the war."

A total of 221 Israeli troops have been killed in Gaza since the ground operation began late last year, according to the IDF.

-ABC News’ Yael Benaya, Jordana Miller, Dana Savir, Joe Simonetti and Morgan Winsor

The international medical charity Doctors Without Borders, also known by its French acronym MSF, warned Tuesday that its staff at Nasser Hospital, the largest still functioning in the war-torn Gaza Strip, "report they can feel the ground shaking."

"There is a sense of panic among staff, patients and displaced people sheltering inside the building," MSF wrote in a series of posts on X, the social media platform formerly known as X.

Nasser Hospital is the only major hospital still accessible in the southern Gaza city of Khan Younis, which has been under siege by Israeli forces amid the ongoing war with Hamas, Gaza's militant rulers.

"All the hospital wards at Nasser are full and there is no way to evacuate medical staff and patients safely due to exit routes from the facility being blocked," MSF wrote.

The organization said its "staff fear the fighting, shelling and bombing will get worse and closer to Nasser hospital."

"There has been heavy ongoing bombing mainly in the southern and northern parts of Khan Younis since yesterday evening," MSF added.

-ABC News' Morgan Winsor

President Joe Biden is "under no illusions" about "how difficult" a two-state solution would be after the war in Gaza ends, National Security Council spokesperson John Kirby said Monday.

Kirby’s comments came after Israeli Prime Minister Benjamin Netanyahu said he "firmly" stands by his belief to prevent the establishment of a Palestinian state as long as he’s in power. Biden said Friday, "We’ll be able to work something out."

"When we say two-state solution, what does it actually mean? And there's many different interpretations. There's lots of different ways you can get at that ultimate solution," Kirby said. "And the president, as he has always done, kept an open mind about trying to pursue that."

"If this was easy, I mean, my goodness, we've had a two-state solution for years now," Kirby continued. "It's going to require negotiation, it's going to require sacrifices, again, on both sides. The president understands that."

Kirby kept characterizing Biden’s phone calls with Netanyahu as "good conversations" and said the president is "not going to let go of this."

-ABC News’ Justin Ryan Gomez