The attack was carried out shortly after dawn on Monday. Large explosions and gunfire were also heard in the area.
"There were seven assailants -- two (suicide bombers) died detonating themselves and five others were killed in fighting," Mohammad Ayoub Salangi, chief of Kabul police, told reporters.
"There have not been any casualties to the security forces, and we have not (received) any report of civilian casualties so far."
The Taliban claimed responsibility for the attack.
The militant group said in April that it had begun its ‘spring offensive’ against the US-led foreign forces in the country.
Hashmat Stanikzai, Kabul’s police chief said that a group of attackers “entered a building in Qasaba road, west of Kabul airport, and started sporadic shooting.”
Kabul International Airport is home to the NATO Joint Command headquarters, and all flights in and out of the airport have been canceled due to the attack. Other NATO bases across the Afghan capital were also locked down.
The large NATO headquarters at the Kabul airport runs the day-to-day operations of the foreign forces in Afghanistan.
The Afghan capital last came under attack on May 24, when the Taliban militants carried out an assault on a compound of the International Organization for Migration (IOM).