It was the first confirmed report of deadly Taliban infighting after an announcement last month that Mullah Omar had been dead for more than two years. Mullah Omar's family objected after his former deputy, Mullah Akhtar Mansoor, was named the new Taliban leader and rivalries have spilled into violence, said Ahmad Rabbani, head of a committee trying to reunify the group.
The five deaths came after Taliban commander Mullah Mansoor Dadullah, loyal to Mullah Omar's family, led hundreds of gunmen against Mansoor supporters in the southern Afghan province of Zabul, where the Taliban have long had a fighting presence, Rabbani said.
Rabbani said his committee hoped to reach a decision on who should lead the Taliban whose leaders have been based in Pakistan since their regime was overthrown in a US-led invasion in 2001 by Tuesday.
Meanwhile, at least 13 police were reported killed in separate attacks in eastern and southern Afghanistan.
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Insurgents have intensified attacks on police checkpoints in recent months, as they typically have few men and are vulnerable. Casualties have soared.
Separately, Ensafi said an Afghan forces airstrike killed 16 insurgents and wounded 17 late yesterday in Ghazni's capital.
The war with the Taliban has been particularly tough this year for Afghan forces, who are fighting without international combat troops backing them up after the US and NATO pulled out last year.