While extensive, international negotiations have now led to the release of four hostages captured by Hamas, scores of foreign nationals in Gaza, including as many as 600 Americans, are still being blocked by the U.S.-designated terrorist group from crossing into Egypt, according to Biden administration officials.

"To date, at least, Hamas has blocked them from leaving, showing once again its total disregard for civilians of any kind who are stuck in Gaza," Secretary of State Antony Blinken said in a televised interview Sunday.

On Monday, State Department spokesman Matthew Miller clarified that the U.S. now assessed that after weeks of negotiations with Egypt and Israel aimed at securing safe passage for the Americans, only Hamas stood in the way.

"We do believe that Egypt is ready to process American citizens if they can make it to Egyptian authorities. Hamas just has to stop blocking their exit," Miller said.

Miller also said that while U.S. officials were not in direct communication with Hamas, they have been urging Hamas to step aside in messages sent through "a number of partners."

The Biden administration has been working since soon after the Oct. 7 attacks on Israel to reopen the Rafah gate -- the sole border crossing between Gaza and Egypt -- in order to move aid into the area and allow foreign nationals to leave.

While a limited number of trucks carrying food, water and medicine were able to enter Gaza for the first time on Saturday, so far none of the foreign nationals has been allowed to leave.

Miller explained that "a number of civilians, some American citizens" flocked to the Gaza side of the Rafah crossing when it was first opened, but none were able to leave because Hamas "was there blocking anyone from coming through the gate from the Gaza side out to the Egyptian side."

According to U.S. officials, the Egyptian government has also been hesitant to allow civilians to exit Gaza through the Rafah gate because of the country's intense concern over security threats posed by terrorist activities on the Sinai Peninsula.

Egyptian officials are also likely eager to avoid the optics of thousands of people pouring across the border from Gaza -- wary the country might appear complicit in what its president and other Middle Eastern leaders have said would be an "ethnic cleansing" of Gaza.

While securing Egypt's cooperation in eventually facilitating the departure of American citizens would be a diplomatic achievement for the administration, it does not yet appear that Cairo has signaled it will extend the same opportunity to the parents, children, siblings, and partners of U.S. nationals in Gaza.

Miller said it was still the administration's goal that the immediate family members of American citizens crossing through the Rafah gate would be allowed to depart as well, but that it was "an ongoing conversation" with Egypt.

With a potential Israeli ground incursion looming, the already dire circumstances facing Americans and their loved ones inside Gaza may soon get even worse.

Abood Okal, a 36-year-old American, has been stranded in Gaza with his wife and 1-year-old son since the beginning of the Israel-Hamas war, told his lawyer, Sammy Nabulsi, that the family has been huddled in a home with 40 other people, sleeping on the floor, sharing meager amounts of food, and that for an entire day, they had been forced to drink salt water to survive.

Nabulsi said in an interview with ABC News Live on Monday that Okal's family had been instructed by the State Department to go to the Rafah crossing four different times, but on each occasion no one had been allowed to pass through the gate.

"I think the holdup is the United States isn't focused on this effort at all," said Nabulsi. "It's unacceptable to me. It should be unacceptable to every single American citizen is this entire country."

Although the State Department asserts that Hamas is preventing them from fleeing to safety, Miller said Americans stranded in Gaza are "in a different situation" from the around 220 individuals the Israeli Defense Forces believes are still being held hostage by the group.

"I am not at all trying to minimize the situation," Miller said, acknowledging Americans like Okal and his family are facing "deplorable" circumstances and vowing that U.S. officials are "working intensively' to get them out.

The administration has not provided any number or estimate of how many of the 500 to 600 Americans thought to be trapped in Gaza have reached out to the State Department for help.

"We have a list of Americans who are registered with us, and when we have any information about the possibility of transiting outside of Gaza, we're providing it to all of them," Miller said.