Sixteen militants were killed and 10 others wounded as Afghan Special Operations Forces conducted overnight operations in Seh Darak, Enayat and Zakhil localities in Kunduz city, 250 km north of Kabul, the official told Xinhua news agency.
Kunduz city has been the scene of sporadic clashes in recent days as Taliban militants have tried to take control of city.
Clean-up operations, including night raid operations, will continue before the city is cleared of the militants, the official said.
The operations had slowed down as the Taliban militants were using residential houses as trenches, he said, adding that no casualties were reported on the side of the security forces during the fighting.
In addition, eight Taliban militants were killed and five others wounded when Afghan National Army troops exchanged fire with militants in many locations in Kunduz city late Friday night, an army source said.
Taliban militants fighting the government forces have not made any comments on the incidents so far.