Several other people were injured in the conflicts in at least three provinces, China's Xinhua News Agency reported.
Authorities said one Taliban fighter died and two others were injured when an improvised explosive device they were burying along a roadside in western Herat province detonated prematurely early Monday. The bomb reportedly was to have targeted security forces.
Seven Taliban fighters died in a similar incident in Helmand province.
Also in Helmand, three civilians were wounded in the Marja district when a tractor rolled over an IED early Monday, said provincial government spokesman Omar Zwak.
Eleven militants were killed and a police officer wounded in an overnight clash in the Nad Ali district, Zwak said. In a separate incident Sunday night, three police officers were wounded in an exchange of gunfire with militants.
Eleven Afghan police officers were killed in Kandahar province when militants launched an attack on a checkpoint near the Pakistan border, officials said.
Border patrol officials Gen. Tafsir Khan confirmed the attack and the Taliban claimed responsibility through spokesman Qari Yousuf Ahmadi. He said all security forces at the post were killed and Taliban members seized their weapons.