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.