Taliban Launch A Large Scale Attack On Kabul's International Airport
Kabul police told the BBC that the gunmen were attacking the airport from a five-storey building under construction.
It is not yet known if there are any casualties.
A BBC correspondent at the scene says a police rapid reaction force is battling to regain control of the area.
All flights have been cancelled in and out of Kabul international airport, which is home to a large Nato-led military base.
Witnesses reported the sound of explosions and gunfire coming from the airport shortly after dawn on Monday.
No group has so far said it carried out the attack.