The US Defense Department said 13 were killed after two suicide bombers deployed by the Afghanistan branch of the Islamic State group detonated their bombs by a key gate into the airport and at a nearby hotel used for staging evacuees.
The initial toll was 12, which increased when an additional service member died from his wounds.
Ten of those killed and several wounded were US Marines, Marine Corps spokesman Major Jim Stenger said in a statement.
The two-decade war has cost 1,909 US military lives in combat. The heaviest losses came on August 6, 2011, when insurgents shot down a Chinook transport on a nighttime mission in Wardak province southwest of Kabul.