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

Sahar Amer is married with two children, ages 2 and 4, and lives in a camp in Khan Younis in southern Gaza.

"Since the beginning of the war, I have believed that this camp was safe -- a very densely populated area, and my relatives chose me as our home to seek refuge in to escape the bombing," Amer, 28, told ABC News.

"Everything has been difficult to obtain since the beginning of the war: food, water and treatment," Amer said. "But unfortunately, what happened a week ago changed everything. The area became unsafe due to the sudden entry of [Israeli] tanks behind Nasser Hospital, which is only several meters away from us."

"During the Israeli army’s incursion behind the hospital, we lived a very terrifying night due to intense artillery shelling," she said. "I could hear the sounds of bullets flying."

"Then the quadcopter planes started shooting at citizens. One time I was on the roof of the house with my children and we miraculously escaped death," Amer said.

"I did not expect the army to infiltrate in this way," she said, noting that her family "took refuge with us, believing that this area is safe and that the army cannot encircle the camp like this."

One night she headed home and said she found tanks "stationed west of the camp and surround[ing] the place."

"I felt very afraid that the tanks were approaching my house,” she said. “I was hugging my children.”

Amer wanted to leave her house, but couldn’t find a car. So she took her children and they fled on foot.

"When I approached the road, a tank appeared … and prevented us from passing through,” she said. "I returned home crying and afraid that our fate will be death like the residents of other areas. I sent a message to my mother and sister to pray for me to be saved."

"I went out with great difficulty the next day. I left my home crying. I do not want to be displaced -- I want to remain safe in my home." she said. "I hope the war will end -- there is enough death and destruction."

-ABC News’ Ruwaida Amer

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