The clash took place in Dawlat Abad district after the commandos and local troops launched a clearing operation, TOLO News quoted the official as saying, adding that six policemen were also injured in the violence.
The security forces have retreated from the centre of the district following the heavy clashes are now stationed in Qaramqol district, the official said.
The centre of Dawlat Abad district fell to the Taliban a week ago following heavy clashes.
Violence remains high in the country amidst a stalled peace process.
Official sources on Wednesday reported fighting between Afghan security forces and the Taliban in at least 80 districts in a day.
According to the sources, over 100 Taliban fighters and 90 security force members were killed during this period.
Neither the Taliban nor the government have provided the exact number of casualties.
Data collected by TOLO News reveal that centres of at least 30 districts have fallen to the Taliban since the beginning of the official withdrawal of the US and other NATO troops on May 1.