The United Nations Relief and Works Agency for Palestine Refugees in the Near East said Wednesday that its training center in Khan Younis where hundreds of displaced people are taking shelter "has just been hit" as fighting escalates in the southern Gaza Strip.

In a series of posts on X, the social media platform formerly known as Twitter, the director of UNRWA’s affairs in Gaza, Tom White, wrote that "two tank rounds hit building that shelters 800 people - reports now 9 dead and 75 injured." White added that people remain trapped inside as teams from UNRWA and the World Health Organization are "trying to reach the centre," but the "agreed upon route with Israeli Army [is] blocked with earth bank."

It was unclear who was responsible for the attack on the shelter as Israeli forces battle Gaza’s militant rules, Hamas. There was no immediate comment from either of the warring sides.

-ABC News' Joe Simonetti and Morgan Winsor

National Security Council spokesperson John Kirby said the U.S. is "in serious discussions about trying to get another pause" in fighting between Israel and Hamas to secure the release of remaining hostages, but Kirby said he could not confirm specific reports of a possible framework.

Asked about reports that Israel has proposed a two-month cease-fire to release all hostages, civilians and soldiers, and asked if the U.S. was actively working to drum up support for it, Kirby said he was "not able to confirm those specific reports."

Kirby did note that President Joe Biden’s Middle East coordinator, Brett McGurk, is currently in the region, in part to discuss a hostage deal.

"Certainly, one of the things he's in the region talking about is the potential for another hostage deal, which would require a humanitarian pause of some length,” Kirby said. “He’ll also be talking about a range of other issues, including humanitarian assistance."

Kirby also said it was "possible" that an extended pause could be a path to changing the nature of the war, but he stressed that the focus remains getting the hostages released.

-ABC News’ Molly Nagle

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