Israel-Gaza updates: IDF releases seized Hamas 'psychological terror' video

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

A United Nations worker was killed and another injured after their vehicle was struck in Gaza on Monday, the organization said.

The staff members of the U.N. Department of Safety and Security were traveling to the European Hospital in Rafah when their U.N. vehicle was struck, the U.N. said.

Details on the incident were not immediately available. The U.N. said it is still gathering information.

U.N. Secretary-General António Guterres has called for a full investigation, his spokesperson said.

"Humanitarian workers must be protected," Guterres said on X. "I condemn all attacks on U.N. personnel and reiterate my urgent appeal for an immediate humanitarian ceasefire & the release of all hostages."

More than 190 U.N. staff members have been killed in Gaza since Oct. 7, according to Guterres.

Almost 360,000 people have fled from the southern Gazan city of Rafah since Israel issued an evacuation order last week, the United Nations agency operating in Gaza said on Monday.

"There's nowhere to go," the U.N. Agency for Palestine Refugees said on social media. "There's NO safety without a cease-fire."

The agency had said Sunday that 300,000 people had evacuated the city as Israel weighs a full-scale invasion.

-ABC News' Kevin Shalvey