The United States says it is engaging directly with the Taliban to secure safe passage for "everybody" who is trying to get to the Kabul airport.
The U.S. is also reaching out to dozens of countries to host at-risk Afghans while accelerating the evacuation of American citizens, diplomats and Afghan asylum-seekers.
"Our team in Doha and our military partners on the ground in Kabul are engaging directly with the Taliban to make clear that we expect them to allow all American citizens, all third country nationals and all Afghans who wish to leave to do so safely and without harassment," Deputy Secretary of State Wendy Sherman said.
She spoke during a Wednesday press conference amid reports that the Taliban were blocking Afghans from reaching the Kabul airport. At about the same time, the U.S. Embassy in Afghanistan issued a security alert warning it "cannot guarantee safe passage" to the Kabul airport.
By late Wednesday, nearly 6,000 people had been evacuated since the collapse of the Afghan government, according to a White House official.
"In the last 24 hours, U.S. military flights evacuated approximately 2,000 more people. Over the last several days, we have processed more than 4,840 people for evacuation," Sherman said.
WATCH: Afghan evacuations
Two thousand Afghan Special Immigrant Visa (SIV) applicants have been relocated to the U.S. in recent weeks, according to the State Department.
In an interview with ABC News’ George Stephanopoulos on Wednesday, U.S. President Joe Biden said U.S. troops will stay in Afghanistan until all Americans are evacuated even if it is past the August 31 deadline.
"If there's American citizens left, we're going to stay there until we get them all out," Biden told ABC News.
But as the planned U.S. military withdrawal nears, Washington’s diplomatic presence in Kabul appears uncertain.
The State Department said the U.S. Embassy, which has been relocated to the Kabul airport, will continue to function "as long as it possibly can."
"The fact of the matter is, we are going to do as much as we can for as long as we can. If the window is two weeks, we will make the most of that window. If the window is slightly longer, we will make the most of that window," said State Department spokesperson Ned Price on Wednesday during a briefing.
Some critics say the U.S. appears to be ceding the possibility of influencing events in Afghanistan going forward.
"By pulling diplomats out and leaving only a skeletal crew to manage day-to-day consular affairs, the U.S. is making it clear that it is unable and/or unwilling to carry out a prioritization of diplomatic means or entertain any opportunities for compromise," said Azza Karam, secretary general of Religions for Peace, a nonprofit organization that provides a platform for multireligious leadership.
Rights organizations and analysts painted a bleak picture, warning of an emerging refugee crisis.
Refugee International and other groups have called on the U.S. to commit to resettling up to 200,000 Afghan refugees.
"The fall of Afghanistan to the Taliban will likely spark a reinvigorated refugee — and broader forced displacement — crisis in a country where persistent humanitarian needs have doggedly accompanied fragile progress. Unless the United States and its partners sufficiently respond to this next big refugee crisis, millions of displaced Afghans in 2021 could make the 2015 migration crisis seem like a geopolitical walk in the park," said Erol Yayboke, director of the Project on Fragility and Mobility at the Washington-based Center for Strategic and International Studies.
Early Wednesday, U.S. President Joe Biden and Vice President Kamala Harris received a briefing by the White House national security team on the situation in Afghanistan.
“They discussed efforts to accelerate evacuations of U.S. citizens, Special Immigrant Visa (SIV) applicants and other vulnerable Afghans, and to facilitate safe passage to Hamid Karzai International Airport,” plus the monitoring of potential terrorist threats, a White House official said.
In a separate call, the White House said Biden spoke with German Chancellor Angela Merkel on “the need for close coordination on the provision of humanitarian aid for vulnerable Afghans in country as well as support for neighboring states.”
The White House said the U.S., Germany and Britain have agreed to hold a virtual Group of Seven leaders meeting next week to discuss a "common strategy and approach.”
Tuesday, Secretary of State Antony Blinken spoke with his counterparts from U.S. allies, including Canada, Kuwait and Qatar, about the rapidly evolving situation in Afghanistan, as well as efforts to bring vulnerable Afghans to safety.
As the U.S. continued to evacuate Americans and diplomats, Kuwait and Qatar said they were facilitating the transit of U.S. citizens and embassy personnel through their countries.
Canada was also helping to host at-risk Afghans.
"The secretary expressed his profound appreciation to Canada for resettling 20,000 vulnerable Afghans and for Canada’s ongoing coordination with international efforts to address the situation in Afghanistan,” according to a State Department statement.
U.S. Undersecretary for Political Affairs Victoria Nuland was said to be leading the U.S. outreach efforts to dozens of countries, including in the Balkans and Africa, to host Afghan refugees.
“We deeply appreciate Uganda’s generous offer of assistance to host Afghanistan evacuees on a temporary basis. We have not yet made a final determination of assistance requirements in Uganda and discussions with the government of Uganda concerning the situation in Afghanistan are ongoing,” a State Department spokesperson told VOA.
White House Correspondent Patsy Widakuswara contributed to this report.