Eighteen aircraft will transfer people to third countries from safe sites outside Afghanistan, the Pentagon said.
Many thousands of Afghans are crowded outside Kabul airport, desperate to flee the country after the Taliban swept to power on 15 August.
President Joe Biden said on Sunday that the US had evacuated nearly 28,000 people in the past week.
"There is no way to evacuate this many people without pain and the heart-breaking images you see," Mr Biden told reporters at the White House, adding: "We have a long way to go and a lot can still go wrong."
At least 20 people have died as thousands queue outside Kabul airport, a Nato official told Reuters news agency, with reports that some were being crushed to death.
The scene on Sunday was reportedly calmer than in previous days.
UK Armed Forces Minister James Heappey said the Taliban were now marshalling people into queues at Hamid Karzai International Airport, making the process faster for those hoping to leave.
The UK has evacuated 5,725 people since 13 August, the Ministry of Defence (MoD) said late on Sunday.
The UK has more than 1,000 Armed Forces personnel deployed in Kabul.