New York Times reported Sunday night that according to military sources, about 12 rockets landed around Camp Bastion, an airbase in Helmand province, in late July.
In the past week, several rockets were fired at Camp Dwyer, a US base also in Helmand.
However, a Taliban commander rejected the claims.
One military official told the New York Times the rocket strikes may have been carried out by a Taliban faction that is against the Doha agreement.
No casualties were reported in either attack.
The February agreement between the US and Taliban stipulates that the insurgent group would refrain from attacking US or NATO facilities.