The militants launched the attack in Dasht-e Archi district overnight, Safiullah Amiri, a member of the provincial council, said on January 29.
Eight soldiers and at least four policemen were injured in the fighting while at least three others were taken captive by the Taliban, according to Amiri and an unidentified security source.
District Governor Saduddin Sayyed said the clashes continued through the morning.
Sayyed said the attackers seized weapons but said the checkpoints were now back under the control of government forces.
The Taliban claimed responsibility for the attack, which came a day after at least 10 police officers were killed in a Taliban assault on a police station in the northern province of Baghlan.
Meanwhile, Afghan special forces freed 62 security forces from a Taliban prison in the northwestern province of Badghis, the Defense Ministry said on January 29.
It said five militants were detained during the overnight operation, while several others were killed or wounded.
Najmuddin Burhani, a spokesman for Badghis’s governor, told RFE/RL that those freed had been held by the militant group for more than a year.
The Taliban has not immediately commented.
U.S. and Taliban negotiators earlier this month kicked off another round of talks aimed at putting an end to the 18-year war in Afghanistan.