"Mullah Omar's close aide Mullah Mohammad Rasoul, who refused to make allegiance to Mansoor, was chosen by his supporters as the supreme leader of Taliban fighters on Monday," Tolo television channel reported in its news bulletin.
Neither the Taliban nor the Afghanistan government have commented on the report.
In the wake of the confirmation in late July of the death of Taliban leader Mullah Omar, The Taliban militants divided into two factions of supporters and opponents of Mullah Akhatar Mansoor.
The opponents close to Mullah Omar led by Mullah Yaqub, son of Mullah Omar, opposed Mullah Akhtar Mansoor's legitimacy as Amirul Momin (the supreme leader), and the challenge practically divided the armed group.
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According to media reports, Mullah Manan Niazi has been appointed the spokesman and Mullah Mansoor Dadullah the deputy leader of the splinter group of the Taliban.