According to the statement, eight Taliban were killed and 12 others wounded in the air strikes yesterday.
Those killed include Janat Gul and Abdul Sattar, two commanders of Taliban, the statement adds.
However, Taliban have not yet commented on the report.
The air strikes come a day after six insurgents were killed in a clash with security forces in Kamdish district of Nooristan province. According to Khaama press.
An official said the militants had just crossed the border into Afghanistan from across the Durand Line.
Nooristan which is on the border with Pakistan is one of the comparatively restive areas of Afghanistan where Taliban are actively operating.