While White House press secretary Jen Psaki said the U.S. military is continuing to evacuate Americans for as long as it can ahead of Biden’s deadline, she was asked if the White House has a message to Americans who may get left behind that still want to get out.

"Our message is our commitment is enduring, and our commitment does not waiver as we bring our men and women from the military home," Psaki said.

She went on to outline a few ongoing steps the Biden administration is taking to ensure evacuations beyond Aug. 31, leaning heavily on Secretary of State Antony Blinken meeting with international partners and their putting pressure on the Taliban to keep the airport in Kabul open for safe passage.

"On Friday, one of the Taliban leaders delivered public remarks conveying that individuals who wish to leave after the 31st would be able to do so. That does not mean we trust what they say, but there is an enormous amount of international leverage," Psaki said. "And there is also of course a discussion about what our diplomatic presence may look like moving forward."

As of Sunday night, there were up to 250 U.S. citizens still in Afghanistan trying to evacuate, a State Department spokesperson told ABC News. There are thousands of desperate Afghans also clinging to hopes of leaving the country under Taliban rule.

"We need to figure out how to work with partners to reopen the civilian airport and ensure that is a mechanism, that is an area where there is mutual interest by the United States, by international organizations like the World Food Program who want assistance in, and by the Taliban to get these airports operational and running," she said.

During a virtual FEMA briefing between Biden and governors and mayors from areas impacted by Hurricane Ida, reporters did not have the chance to ask him questions on Afghanistan in the final hours before his deadline to withdraw U.S. troops.

There are no other public events on his schedule for Monday.

Asked at an afternoon press briefing if Biden will do anything to mark the moment -- the end of America’s longest war -- White House press secretary Jen Psaki said she wouldn’t get into details but that the American people can expect from Biden “in the coming days.”

She also said Biden is staying in touch with the families of 13 fallen service members he met on Sunday at Dover Air Force Base, saying he'll "continue to look for ways to honor them and the lives that were lost last week."

"What role the president plays or doesn't play is probably not front and center for them, but he's only going to do things that are of comfort to the family, are supportive of, remembers the lives that have been lost," she said, on whether Biden would attend any of their funerals.

Asked specifically about the sister of one of the fallen Marines who has publicly criticized Biden, Psaki said Biden takes responsibility but would not comment further on his conversations with families.

"I think the president made clear, as the secretary of state and our national security adviser made clear, that we're all responsible and their response -- they feel responsibility and the buck stops with the president," Psaki said.

Secretary of State Antony Blinken is scheduled to speak at 5 p.m. on “our efforts in Afghanistan since August 14 and the way forward," according to the State Department, following his virtual meeting with allied nations on Afghanistan.

The United States, United Kingdom and France are seeking to pass a United Nations Security Council resolution calling on the Taliban to "live up to its commitment to ensuring safe passage" for Afghans and others who want to leave Afghanistan, according to three UN diplomats who spoke to reporters on Monday.

It's not clear what impact a Security Council resolution would have on the Taliban's actions other than even more forcefully showing the international consensus behind holding the Taliban to its assurances on safe passage. The group has, indeed, sought international recognition as it assumes power.

The Biden administration had already lined up more than 100 countries to sign onto a joint statement that calls on the Taliban to allow Afghans and foreign nationals who have travel authorization from abroad to leave. Notably, Russia and China -- both Security Council members who have flirted with recognizing the Taliban -- were not among those who have signed on.

The draft of the UN Security Council resolution being discussed Monday stopped short of calling for a "safe zone" and would instead rely on the Taliban itself to allow for safe passage. The resolution also calls for the Taliban to allow "unhindered humanitarian assistance" to continue -- from the UN and other organizations -- and "underscores, in strong terms, the urgent need to tackle the serious terrorist threat in Afghanistan."

The three diplomats did not indicate that there would be any sort of enforcement mechanism associated with this resolution.

The White House has added a virtual meeting between Biden and FEMA Administrator Deanne Criswell, as well as governors and mayors from U.S. areas impacted by Tropical Storm Ida, as the military enters its final hours in Afghanistan.

Pool reporters will be allowed in for the top of the meeting, but it’s unclear if they will be able to ask Biden questions on Afghanistan or whether he would answer them.

At an event related to then-Hurricane Ida at FEMA headquarters in Washington on Sunday, when a pool reporter asked about Afghanistan, Biden said, "I’m not going to answer on Afghanistan now," before walking out.

Secretary of State Antony Blinken is scheduled to speak on Monday evening after hosting a virtual summit with allies on Afghanistan. White House press secretary Jen Psaki is scheduled to brief reporters at 2 p.m.