No civilians were harmed and no damage to the airport occurred, according to multiple officials, but the attack briefly forced flights to be suspended.
The attack began when a suicide car bomb was detonated on a road near the airport about 4:30 a.m., after which the assailants took over the fifth floor of a building under construction in Qasaba, a cluster of structures less than a half-mile from the air facility.
The attackers started firing heavy and light weapons including rocket-propelled grenades toward the side of the airport used by the U.S.-led international military coalition.
The Afghan police's rapid response force surrounded the building and international soldiers also were seen in the area, according to witnesses. The sound of gunfire continued for four hours before the assailants inside the building were shot dead by security forces, officials said.
Sediq Sediqqi, spokesman for the interior ministry, said a total of six attackers were involved and that all spoke Urdu, the language of neighboring Pakistan. Afghan officials and analysts allege that a recent rise in violence in eastern Afghanistan is the result of militants from Pakistan crossing the border to escape a Pakistani military offensive.
One police officer was wounded, said Hashmat Stanikzai, spokesman for Kabul police.
The Taliban claimed responsibility for the attack, which they said targeted the military side of the airport.