Mohammad Reza Ghafori, a spokesman for the provincial governor, said today that the fighting, which began the day before, has killed 76 Taliban fighters and 15 from the IS affiliate.
He says the IS militants seized two districts from the Taliban.
The Taliban and IS are both fighting to overthrow Afghanistan's US-backed government and impose a harsh version of Islamic rule, but they are bitterly split over leadership and tactics.
The IS affiliate is largely made up of disgruntled former Taliban fighters.
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