The US has drafted commercial airlines to help with the evacuation effort.
Aircraft from Delta, United Airlines and others will help fly those already evacuated from Afghanistan to final destinations.
Tens of thousands of Afghans are still racing to flee the country, a week after the Taliban seized control.
At least 20 people have died in the chaotic scenes in and around the airport since Sunday, a Nato official told Reuters.
Biden is facing growing calls to extend evacuations beyond the end of August.
The European Union's foreign policy chief says it would be "impossible" to evacuate all Afghans with travel permits by 31 August.
But a UK minister says evacuation efforts are improving, with the Taliban marshalling crowds.
