Members of Mullah Omar's family have rejected the appointment of the new leader, his deputy Mullah Akhtar Mansoor, demanding a new and wider vote.
The Taliban have issued a series of statements aimed at deflecting the dissent and their spokesman has denied that a new vote would be held.
Today, about 200 high-ranking Taliban members and commanders met in the Pakistani city of Quetta with Mullah Omar's brother Mullah Abdul Manan and son Mullah Yaqub, said Mullah Hameedullah, a member of the Taliban's unity council, which effectively functions as a dispute resolution committee.
Mullah Yaqub confirmed he had attended the meeting but gave no further details.
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The meeting follows days of building animosity as cracks appear in the Taliban's carefully guarded veneer. Some within the Taliban are questioning the legitimacy of Mullah Mansoor, who has acted as a proxy leader in Mullah Omar's name since he died in April 2013.
The statement, signed by spokesmen Zabihullah Mujahid and Qari Yusouf Ahmadi, called on supporters to "help write messages and letters on social media" to show a united front.
The Taliban last week confirmed the death of Mullah Omar, the reclusive, one-eyed leader who ruled Afghanistan from 1996-2001 and sheltered Osama bin Laden, after it was initially announcement by Afghanistan's security agency.
Mullah Mansoor was chosen to succeed him by the insurgent group's seven-member supreme council.
Lately, Taliban fighters have been defecting to the Islamic State group in northern Kunduz province, and the two rival militant groups have increasingly fought it out there.
The Kunduz governor's spokesman, Abdul Wadood Wahidi, said about 50 Taliban fighters in the province's Archi district joined the IS three days ago after being offered money. This set off fierce fighting between the rivals and the Taliban arrested the defectors, he said.
The incident, Wahidi said, "shows there is a fracturing among the Taliban ranks."
The Afghan government, meanwhile, banned any public mourning for Mullah Omar, saying late Monday that it would cause "anguish and humiliation" for those who have lost loved ones in the war with the Taliban.