Mullah Mansoor Dadullah was lured into a trap and killed by members of the main Taliban group in the Khak-e-Afghan district of southeastern Zabul province, the provincial deputy police chief Gulam Jelani Farahi said.
Dadullah who acted as a deputy to the splinter faction's leader Mullah Mohammad Rasool was killed late Wednesday, he said.
Farahi's claim couldn't be independently confirmed and the breakaway faction did not report it. The area of inter-Taliban fighting is inaccessible to reporters.
"When the other bodyguards were not paying attention, this Mansoor man opened fire on Dadullah and killed him," the Taliban commander said, speaking on condition of anonymity because the group had not authorized him to speak to the media.
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Rasool's faction had disputed the legitimacy of Mullah Akhtar Mansoor, who became Taliban leader after the announcement in July that founder Mullah Mohammad Omar was dead.
Rasool was elected as head of the breakaway faction on Nov. 1. It is not known how many Taliban commanders or fighters are loyal to him.
Afghan officials have said the IS presence in Zabul is mainly made up of former members of the Islamic Movement of Uzbekistan who have declared allegiance to IS, which controls about a third of both Iraq and Syria and has ambitions to pull Afghanistan into its orbit.
It remains unclear how Dadullah's death, if confirmed, will affect the inter-Taliban fighting, which has been raging for almost a week now.