Manan Niazi, a spokesman for the dissidents, says that Mullah Mohammad Rasool has been voted in as the Taliban's "supreme leader."
It's unclear how many followers the splinter group has but Thursday's statement is a reflection of deep divisions among the Taliban, who have been waging war on the Kabul government for 14 years.
The differences among various Taliban leaders have been festering since July, when Afghanistan's intelligence service announced the death of Mullah Mohammad Omar, the group's founder and leader.