According to the Tolo News, the Afghan officials confirmed that the clashes took place in Check district of the province after a group of Taliban insurgents attacked police check posts.
A spokesperson for the provincial governor Naqibullah Amini said, "In a separate incident, Taliban fired a missile in the city which killed two civilians."
However, he did not provide further details of the attacks.
Taliban has not commented on the incident so far.
Earlier this week, a deadly fight between the two factions of Taliban in western Heart region of Afghanistan left 50 insurgents dead.
The latest clashes took place between the supporters of Taliban supreme Mullah Hebatullah Akhundzada and dissident Taliban leader Mullah Mohammad Rasool.
In March 2016, at least 26 Taliban militants were killed in the infighting among Mullah Samad and Mullah Nangialai in western Herat province of Afghanistan. (ANI)