General Abdul Ghafar Safi, the provincial police chief, says six other policemen were wounded in the attack late yesterday in Nawa district, where clashes were still underway early today.
Taliban spokesman Qari Yusouf Ahmadi claimed responsibility for the attack.
In the neighbouring Uruzgan province, the Taliban attacked a checkpoint in the provincial capital, Tarin Kot, killing a policeman and igniting clashes that killed 15 of the insurgents, according to Dost Mohammad Nayab, spokesman for the provincial governor. He said another three policemen were wounded.
The United States has about 8,400 troops in Afghanistan, who support local forces and carry out counterterrorism operations.