Khalil Asir, spokesman for the police headquarters of Takhar province said that the operations were conducted in Ishkamish and Khwaja Ghar districts.
Asir identified the dead Taliban commanders as Qari Salahuddin the Taliban so-called governor for Ishkamish District and Qari Ibrahim another Taliban commander.
He said that 25 other militants were killed and 19 wounded in these operations.
The police spokesman confirmed the martyrdom of two policemen in these operations.
He said that three other policemen also sustained injuries in the exchange of fire with militants.