The Simurgh operation was launched in the Azra and Hesarak districts July 22, said Dawlat Waziri, deputy spokesman for the ministry.
Security forces seized weapons and explosives as part of the offensive, Khaama Press reported Monday.
Gen. Afzal Aman said the operation was launched in response to a recent increase in the number of militants in the Azra district.
On Sunday, in southern Zabul province's Shahjol district, a police commander and two officers were among at least nine people killed in an explosion, local police said.
The main target of the attack was the commander, identified only as Mujahid, police said.
Deputy Provincial Gov. Mohammad Jan Rasouliar said at least six Afghan civilians also died in the attack and 12 were injured.
Taliban militants claimed responsibility for the attack, Khaama Press reported.