About 450,000 Palestinians have been displaced from Rafah, fleeing to safety, according to the U.N. Relief and Works Agency for Palestine Refugees in the Near East.

"Inland in Rafah is now a ghost town. It’s hard to believe there were over one million people sheltering here just a week ago,” UNRWA spokesperson Louise Wateridge said. "People face constant exhaustion, hunger and fear. Nowhere is safe. An immediate ceasefire is the only hope."

The development comes as airstrikes continued to hit northern and southern Gaza Tuesday. The Israeli military said it had hit 120 targets in the last 24 hours.

-ABC News' Will Gretsky

The International Court of Justice said it will hold hearings over Israel's attacks on Rafah during the war in Gaza, after South Africa sought new emergency measures as part of its ongoing case accusing Israel of violating the Genocide Convention in its offensive on Gaza.

Hearings will be held on Thursday and Friday in the Hague.

South Africa first brought the case before the ICJ in December alleging Israel violated its obligations in its offensive with regard to Palestinians in the Gaza Strip.

National security adviser Jake Sullivan stressed the U.S. is working "urgently and relentlessly" to get a hostage deal in place, but did not have any major progress to share Monday.

Sullivan noted that he met with the families of American hostages this past Friday, and that "they know how hard the president is working on this."

On where the hostage negotiations stand currently, Sullivan turned to the architect of the Good Friday agreement in Ireland.

"Sen. [George] Mitchell said quite famously, "'Negotiations are 1,000 days of failure and one day of success.' And right now, we're in the former days rather than the latter day," he said.

"[T]here could be a cease-fire tomorrow if Hamas simply released women, wounded and elderly hostages, all innocents. Israel put a forward-leaning proposal on the table for a cease-fire and hostage deal. The world should be calling on Hamas to come back to the table and accept a deal," Sullivan said.

-ABC News' Molly Nagle

The State Department on Monday said it was aware of reports that U.S. doctors were trapped in Gaza, and that it's been working with Israel to reopen the Rafah gate so U.S. citizens and other foreign nationals can leave.

"I can say that we're aware of these reports of U.S. citizen doctors and medical professionals currently unable to leave Gaza," principal deputy spokesman Vedant Patel said. "As I said before, we don't control this border crossing. And this is a incredibly complex situation that has very serious implications for the safety and security of U.S. citizens. But we're continuing to work around the clock with the government of Israel, with the government of Egypt, to work on this issue."

He added, "Rafah is a conduit for the safe departure of foreign nationals, which is why we continue to want to see it get opened as swiftly as possible."

The State Department said it does not have an estimate of Americans still trapped in Gaza, but that it's helped 1,800 U.S. citizens and legal permanent residents to depart Gaza so far.

"Unfortunately, this is not a border crossing the United States controls but we are continuing to work around the clock with the government of Israel, with the government of Egypt on whatever we can do to make sure that Rafah gets open. … We need to see Rafah open as soon as possible," Patel said.

-ABC News' Anne Flaherty

House Republican Conference Chairwoman Elise Stefanik of New York will be giving remarks in the Israeli Knesset on Sunday, according to her office. Stefanik will be the highest-ranking member of the House to visit Israel following the Oct. 7 attack.

Stefanik plans to slam President Joe Biden for recently halting some military aid to Israel, according to excerpts of her speech reviewed by ABC News.

"I have been clear at home, and I will be clear here: There is no excuse for an American president to block aid to Israel," Stefanik will say during the address.

Biden announced the U.S. would withhold certain bomb deliveries to Israel over fear they could be used in Rafah, but the Biden administration informed Congress it's moving forward with more than $1 billion in new arms agreements with Israel.

The congresswoman will address the rise in antisemitism in the U.S., House Republicans' support for Israel and even mention her close ally, former President Donald Trump.

"I have been a leading proponent and partner to President Trump in his historic support for Israeli independence and security," Stefanik will say.

-ABC News' Lauren Peller