The fighting was in a district called Koshtipa, on the border with Turkmenistan, Aminzada said.
Nine other policemen were killed and three wounded in the southwestern province of Farah when the Taliban attacked them, Rohul Amin, the provincial governor, told AFP. Six of the attackers also died in the fighting, he said.
The clash followed fighting earlier in the day when Afghan and US-led troops were called in after intelligence was received of a plan to attack his home, Amin said. Seven Taliban were killed in that exchange, he said.
Elsewhere, in the province of Farah on Friday, a suicide bomber blew up a bomb-filled police vehicle and killed one policeman and wounded two more, the governor said.
The deadliest fighting was on Thursday, when Afghan and US-led troops killed 30 fighters in the southern province of Helmand, in a district where a leading anti-Taliban MP was killed in a bomb attack the same day.
The Afghan army led a joint patrol into an area of Gereshk district where fighters were known to operate and they came under attack, the US military said in a statement.
The "combined element returned fire with small-arms and close air support, killing 30 militants", it said.
The toll was the highest from a single clash announced by the military in more than two months, with Afghanistan gearing up for another year of intense fighting after the winter.
The US military also announced on Friday that six more fighters were killed in operations in Kunar, Logar and Helmand.