Bagram district security chief Zmarai Nasiri said two missiles landed inside the Bagram airfield last night.
Mr. Nasiri further added no casualties or damage to the base have reported so far.
In the meantime Zabiullah Mujahid Taliban group spokesman claimed responsibility behind the incident and said at least three missiles were fired on Bagram air base and claimed that coalition forces have suffered casualties during the attack.
In a separate incident at least five Taliban militants were killed and two others were injured following clashes with the Afghan security forces in northern Parwan province.
A spokesman for the Afghan police forces in the north Ahmad Jawad said the incident took place after a number of Taliban militants attacked a security check post.