The Taliban attacked a police post in the Kajaki district of Helmand province according to a deputy provincial governor.
AP on Friday quoted Mohammad Amir Akhund as saying: "In the couple-of-hours exchange of fire, six Taliban were killed and three were wounded.
"Taliban have control of three villages in the district now. The government forces have not started any operation in these three villages so far."
The province of Helmand is practically lawless and is one of the areas most affected by an increasing number of attacks that are blamed on a Taliban-led insurgency.
Its is the largest producing area of opium in a country that is the largest producer in the world of the drug.
Around 3,300 British troops are due in Helmand in the coming weeks as part of a multinational force that is being deployed to hunt down members of the Taliban and other Islamist groups.
Kajaki is next to the district of Sangin, the scene of the Taliban's biggest attack on a multinational-force base in months when a Canadian and an American soldier were killed on Wednesday.
The attack happened two weeks after the Taliban announced a spring offensive.
An estimated 1,700 people were killed in violence in Afghanistan last year, most of the deaths, double the number of 2004. Most of the deaths were due to the insurgency and most of them were fighters.