Bagram district security chief Zmarai Nasiri said no casualties were reported after two missiles landed inside the airfield Monday, Khaama Press reported Tuesday.
Nasiri said he didn't receive reports of damage to the base.
Taliban militants claimed responsibility for the attack. Spokesman Zabiullah Mujahid claimed at least three missiles were fired toward the air base and coalition forces suffered casualties during the attack.
Also in Parwan province, Afghan police said at least five Taliban militants were killed and two others injured in clashes with the security forces, Khaama Press said.
A security official said the incident occurred after Taliban militants attacked a security checkpoint.