About 114,000 people have fled the country via a US-led evacuation since the Taliban swept back into power two weeks ago, and the operation is winding down despite Western powers saying thousands may be left behind.
What had already been a chaotic and desperate operation turned bloody on Thursday when a suicide bomber from the local chapter of the Islamic State group targeted US troops stopping huge crowds of people from entering the airport.
More than 100 people died in the attack, including 13 US service personnel, slowing down the airlift ahead of Biden's deadline for evacuations to end by Tuesday.
The Pentagon said Saturday that retaliation drone strikes had killed two "high-level" IS jihadists in eastern Afghanistan, but Biden warned of more attacks from the group.
"The situation on the ground continues to be extremely dangerous, and the threat of terrorist attacks on the airport remains high," Biden said.
"Our commanders informed me that an attack is highly likely in the next 24-36 hours."
The US embassy in Kabul later released a warning of credible threats at specific areas of the airport, including access gates.
Late Sunday afternoon, a loud blast was heard coming from the north of the city which a security official in the toppled government said was a rocket hitting a house.
Further details were not immediately available.
In recent years, the Islamic State's Afghanistan-Pakistan chapter has been responsible for some of the deadliest attacks in those countries.
They have massacred civilians at mosques, public squares, schools, and even hospitals.
While both IS and the Taliban are hardline Sunni Islamists, they are bitter foes -- with each claiming to be the true flag-bearers of jihad.
UNTHINKABLE CO-OPERATION
The IS attack has forced the US military and the Taliban into a form of cooperation to ensure security at the airport that was unthinkable two weeks ago.
On Saturday, Taliban fighters escorted a steady stream of Afghans from buses to the main passenger terminal, handing them over to US forces for evacuation.
The troops were seen throughout the civilian side of the airport grounds and annexe buildings, while US Marines peered at them from the passenger terminal roof.
After a 20-year war, the foes were within open sight of each other, separated by just 30 metres.
Also in view of the US troops were the Taliban's "Badri" special forces in American Humvees gifted to the now-vanquished Afghan army.
Taliban spokesman Bilal Karimi tweeted that the group's fighters had already moved into parts of the military side of the airport, but the Pentagon stressed that US forces retained control over the gates and the airlift.
Pentagon spokesman John Kirby said US troops had started withdrawing -- without saying how many were left.
Biden was on Sunday headed to an air force base in Delaware, where the remains of the servicemen killed in Kabul have been transferred, to attend a ceremony and meet with the victims' families.
'HEARTBREAKING'
Western allies that helped with the airlift have mostly already ended their flights, with some voicing despair at not being able to fly out everyone at risk.
The head of Britain's armed forces, General Sir Nick Carter, told the BBC it was "heartbreaking" that "we haven't been able to bring everybody out".
A White House official said 2,900 people were evacuated in a 24-hour period between Saturday and Sunday, a drastic reduction from earlier in the week.
Two Afghan athletes were able to leave last weekend and spent a week in France before a "major global operation" took them to Japan for the Tokyo Paralympics.
There was an emotional welcome for Zakia Khudadadi and Hossain Rasouli at the athletes' village on Saturday night.
"There were lots of tears from everyone in the room," said International Paralympic Committee spokesman Craig Spence.
French President Emmanuel Macron said talks had begun with the Taliban to "protect and repatriate" at-risk Afghan nationals beyond Tuesday.
France and Britain will on Monday urge the United Nations to work for the creation of a "safe zone" in Kabul to protect humanitarian operations, he said.
The UN said it was bracing for a "worst-case scenario" of up to half a million more refugees from Afghanistan by the end of 2021.
At the airport, gone are the crowds of thousands mobbing the perimeter, hoping to be let through and allowed onto a plane.
The Taliban have now sealed off roads leading to the facility and are only letting sanctioned buses pass.
