The U.S. Department of State has facilitated the evacuation of four U.S. citizens across one of Afghanistan's land borders -- the first Americans to leave the country with help from the U.S. government since President Joe Biden ended the massive, chaotic evacuation efforts that closed the country's longest war.

Four Americans made their way across land with Taliban knowledge, according to a senior State Department official, who told ABC News that they evacuated without Taliban interference.

The official declined to say which country they arrived in but added that they were in "good condition" and met by U.S. embassy staff from the local embassy.

While the State Department helped those four evacuate, White House Chief of Staff Ron Klain said Sunday that there were approximately 100 Americans still trying to escape Afghanistan nearly a week after the last U.S. forces departed.

Among those left behind, there are several Americans in the northern city of Mazar-e-Sharif ready to board charter flights that are being blocked by the Taliban, according to several sources. The Taliban has not given permission to the airlines, leaving the potential passengers stuck in the city for days now.

A State Department spokesperson told ABC News on Sunday that they could not confirm the manifests of these flights because there were no U.S. personnel or assets in Afghanistan anymore, but added: "We will hold the Taliban to its pledge to let people freely depart Afghanistan."

- ABC News' Conor Finnegan

The Taliban claimed victory Monday over Afghan opposition forces in Panjshir province, the last pocket of resistance in Afghanistan and the only province that the Taliban had not seized last month.

Taliban spokesman Zabihullah Mujahid issued a statement saying Panjshir was under full control of Taliban fighters.

"We tried our best to solve the problem through negotiations, and they rejected talks and then we had to send our forces to fight," Mujahid later told a press conference in Kabul on Monday.

The Taliban posted photos and videos on social media apparently showing fighters standing at the gate of the Panjshir provincial governor's office and raising the group's flag in the provincial capital.

A spokesperson for the resistance group, the National Resistance Front of Afghanistan (NRF), took to Twitter to deny that Panjshir had fallen.

"Taliban's claim of occupying Panjshir is false," the spokesperson tweeted. "The NRF forces are present in all strategic positions across the valley to continue the fight. We assure the ppl of Afghanistan that the struggle against the Taliban & their partners will continue until justice & freedom prevails."

The Taliban is blocking efforts to get U.S. citizens out of Afghanistan on flights, according to a non-governmental organization arranging travel for some passengers.

Marina LeGree, the CEO of Ascend, told ABC News that the Taliban has prevented 600 people from leaving Mazar-e-Sharif by charter plane for six days.

The NGO is helping 100 of those passengers, none of whom are American, to try to fly out. LeGree said she is aware of 19 U.S. citizens who are trying to leave but Ascend is not overseeing their departure.

"Ascend, an organization dedicated to empowering young women through athletics, has members trying to leave Afghanistan," LeGree told ABC News in a statement Sunday. "We call on the Taliban to honor their commitments and allow these charters to depart immediately."

The affected passengers are either staying at the airport or at nearby hotels, according to LeGree.

The U.S. Department of State did not confirm whether there are Americans on those flights, but said it "will hold the Taliban to its pledge to let people freely depart Afghanistan."

-ABC News' James Gordon Meek, Molly Nagle, Allison Pecorin and Christine Theodorou

As the State Department shifts to help Americans and Afghans left behind evacuate, a senior official conceded the evacuation efforts weren't "pretty, it was very challenging. ... It involved some really painful tradeoffs and choices for everybody involved."

"Everybody who lived it is haunted by the choices we had to make and by the people we were not able to help depart in this first phase of the operation," a senior State Department official who was on the ground at the airport in Kabul told reporters late Wednesday morning.

But the official praised the "heroic" consular officers who processed those who entered the airport and at times walked the line looking through the massive crowds for U.S. passports and Green cards -- and offered some explanations for what went wrong and arguing those crowds outside the gates bordered on "mob violence."

The official said, based on anecdotal evidence, that "the majority" of Special Immigrant Visa holders were left behind -- those Afghan interpreters, guides and others who helped U.S. forces and applied for a visa -- along with their families.

"We feel an enormous commitment to keep faith with all of the people to whom we owe this debt, and we're going to continue to do everything we can in the coming weeks and months to fulfill that commitment and to help those who wish to leave Afghanistan to do so."

The official declined to provide more details on what that looks like just yet.