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The US is in talks with the Taliban over the control of Kabul airport, the State Department said, as thousands attempt to flee the new regime.
Since the Taliban seized power more than a week ago, the situation has been increasingly chaotic, with crowds of people trying to board flights out of the country.
Dozens of civilians have been killed in stampedes amid one of the largest evacuations in history.
“I can acknowledge that this has been a topic of discussion with the Taliban,” State Department spokesman Ned Price said during a press conference on Monday. "It has been a topic of discussion with our allies; it has been a topic of discussion with many of our partners."
Thousands of Americans, Nato coalition nationals and Afghans who have helped Nato are desperately trying to leave through the only airport that is not controlled by the Taliban.
“There is actually agreement between and among all these actors, of course between the United States and our partners and allies, but also with the Taliban, that all of our interests would serve with a functioning airport,” Mr Price said.
A “functioning state and economy” is needed to establish relations with the international community, he added.
A brief exchange of fire broke out at one of the gates into the Hamid Karzai International Airport on Monday. The US military said that none of its coalition forces was injured.
The incident “appeared to begin when an unknown hostile actor fired upon Afghan security forces,” said Navy Capt William Urban, a spokesman for US Central Command, which oversees American military operations in the region.
The incident followed a statement from National Security Adviser Jake Sullivan, who said that Washington is in close co-ordination with the Taliban as it works to evacuate tens of thousands of people from the Kabul airport before the August 31 withdrawal deadline.
“We are engaging with the Taliban, consulting with the Taliban, on every aspect of what’s happening in Kabul right now,” Mr Sullivan said.
During the last 24 hours, US troops have picked up pace to help citizens leave the county. The US has flown about 10,400 people out of Kabul in the last 24 hours by cargo plane, Mr Sullivan said.
Non-US coalition aircraft removed another 5,900 people.
Washington has evacuated or facilitated evacuations involving around 37,000 people since August 14, when the Taliban took control of the country, the Pentagon said. The number is expected to jump to about 42,000 by the end of the month.
The UK said late on Monday that it has flown more than 7,000 people from Afghanistan.
It said the evacuation process would run for as long as the security situation allowed and that no firm date was set for the flights to stop.
Since the Taliban's takeover, employees of the collapsed government, civil society activists and women are among those who are at risk and have gone into hiding or are staying off the streets.