Washington has pledged to evacuate all remaining American citizens, along with 50000 to 65,000 Afghans who worked with the US military and other services BBC reports.
As BBC reports Mr Biden wants US forces out by the end of this month, but up to 15,000 US citizens are stranded in the country.
The US president told ABC News the turmoil in Kabul was unavoidable.
Foreign governments are ramping up the airlift of Western citizens and Afghans who worked with them.
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In total, America has evacuated more than 5,200 people to date, including 2,000 in the last 24 hours.
The Pentagon has told reporters it aims to expand the airlift to 9,000 people a day.
About 4,500 US troops are in temporary control of Karzai International Airport in the nation’s capital, but Taliban fighters and checkpoints ring the perimeter.
Since Sunday 12 people have been killed in and around the airport, a Taliban official told Reuters news agency. The deaths were caused by gunshots or stampedes.
The Taliban are blocking Afghans from entering the airport without travel documents – but even those with valid authorization have struggled.
One Afghan interpreter was reportedly shot in the leg by the Taliban as he tried to reach the airport on Tuesday night for an Australian military evacuation flight. Photos published by SBS showed the man being treated for the gunshot wound by a doctor.
Some US nationals told the BBC’s US partner CBS News they were also unable to enter for scheduled evacuation flights.
Late on Wednesday US time, the US Federal Aviation Administration said domestic air carriers and civilian pilots would now be allowed to fly into Kabul to conduct evacuation or relief flights, as long as they had permission from the US Defense Department
