Splits have emerged at the top of the Taliban following the appointment of Mullah Akhtar Mansour as replacement for Mullah Omar, the movement's founding leader whose death was confirmed last week.
Some top leaders, including Omar's son and brother, have refused to pledge allegiance to Mansour, saying the process to select him was rushed and even biased.
Tayeb Agha, the head of the Qatar political office set up in 2013 to facilitate talks with Kabul, resigned on Monday in protest at Mansour's appointment and today two more members followed suit.
The news, underlining the deepening divisions in the movement, came as militant sources said clerics were leading meetings in Pakistan, where some Afghan Taliban commanders are in hiding, to try to patch things up.
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At one gathering yesterday, Mansour met Omar's brother Mullah Abdul Manan and urged him to accept his leadership to ensure the unity of the movement, miltant sources told AFP.
Omar's son Mullah Yakoub has been touted as a possible alternative leader but a Taliban cadre said some senior clerics are openly opposed to him.
The bid to heal the rifts is expected to drag on for weeks, depriving the Taliban of clear leadership at a crucial moment as it considers whether to pursue the peace process and faces a rising threat from the rival Islamic State group.
Many militants oppose what they see as Pakistan's attempt to force the Taliban into direct peace talks with the Afghan government.
Mansour and his two newly named deputies are seen as close to the Pakistani military establishment, which has historically nurtured and supported the Taliban.