"A group of insurgents attacked Mirzaka district, one policeman was killed and another one injured in the clash and 12 insurgents were killed and six others were injured", the statement read.
The Taliban has not yet commented on the conflict.
Earlier in the day, fifteen members of the terrorist group were killed and six others were wounded in an attack by the NATO-led international forces in the southern Kandahar province, according to the local governor's press office.
Violence has continued in Afghanistan despite the signing of a peace deal between the Taliban and the US in February. The agreement was intended to pave the way for the start of intra-Afghan talks and the eventual withdrawal of US troops from the country.
*Taliban is a terrorist group banned in Russia.