The fighting between the Taliban and Hezb-e-Islami, which began in Baghlan province Saturday, apparently stems from a rivalry over control of local villages and taxes they generate, the BBC reported.
The two groups earlier had been united in opposition to Afghanistan's government and foreign forces in the country.
The fighting killed 40 Hezb-e-Islami and 20 Taliban militants, Baghlan's police chief told the BBC, and the Taliban arrested at least 50 members of Hezb-e-Islami.
The British broadcaster noted Hezb-e-Islami is loyal to former Prime Minister Gulbuddin Hekmatyar, labeled by the United States a "specially designated global terrorist" in 2003.
Hekmatyar's mujahideen faction helped end the Soviet occupation of Afghanistan.
Death and destruction associated with Hezb-e Islami prompted many Afghans to welcome the Taliban, the BBC said.
Hezb-e-Islami is now the second-biggest militant group in Afghanistan, behind the Taliban.
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