The clash erupted between the armed men of Mullah Samad, a commander loyal to Taliban leader Akhundzada, and his rival commander Mullah Nangiali during which 15 insurgents from both sides also sustained injuries, Xinhua news agency quoted an official as saying.
Sporadic fighting was going on between the two sides in the region, the official said.
Taliban militants have yet to make comment.
Akhundzada replaced Mullah Akhtar Mansour who was killed in a US drone attack in Pakistan late in May.
The succession has been challenged by Mullah Rasoul Akhund after which both the sides have been clashed in several provinces.
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