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

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

Relatives of Israeli hostages being held by militants in the Gaza Strip stormed Israel's parliament, the Knesset, in Jerusalem on Monday in protest of the government's failure to bring their loved ones home.

"You will not sit here while our children die," some of the family members yelled while disrupting a finance committee hearing. "What about ransoming captives?"

Israeli Prime Minister Benjamin Netanyahu met with the families of hostages at the Prime Minister's Office in Jerusalem, telling them there’s no "real proposal from Hamas" on the table right now.

"Contrary to what they say, there is no real proposal from Hamas,” he said. “I say this as clearly as I can because there are so many false things that must be tormenting you. In contrast, there is an initiative of ours, and I will not elaborate."

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

The Palestine Red Crescent Society said Monday that it had "completely lost contact with" its teams in the besieged city of Khan Younis in the southern Gaza Strip as Israeli tanks surrounded Al-Amal Hospital, headquarters of the humanitarian organization.

The PRCS added that its ambulances were "unable to reach the wounded" in Khan Younis due to the ground invasion.

"Israeli occupation forces are besieging the PRCS ambulance center, and targeting anyone attempting to move in the area," the organization wrote in a post on X, the social media platform formerly known as Twitter.

The PRCS said it was "deeply concerned" about the safety of its teams as well as people taking shelter at its facilities in the besieged city.

-ABC News' Morgan Winsor