The Taliban promptly denied the claim, dismissing it as propaganda by the Afghan government.
Sultan Faizy, spokesman for Afghan First Vice President Abdul Rashid Dostum, said the shooting erupted on Tuesday night when Mansoor visited Mullah Abdullah Sarhadi in his house in the city of Quetta.
Faizy says there was an argument, followed by shooting that wounded Mansoor and killed six Taliban figures, including Sarhadi. Faizy also says there are reports Mansoor was taken to a hospital but that his condition is unknown.
Pakistani officials said they are not aware of any such shooting incident.
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Mullah Ghafar, a Taliban commander who goes by one name, told The Associated Press that "nothing like this happened" and that the claim was clearly "propaganda" on Kabul's part.
Mansoor took control of the Afghan Taliban in August, after the announcement of the death of the group's founder, Mullah Mohammad Omar. Mansoor's leadership was challenged among some followers, and a breakaway Taliban faction emerged, followed by clashes between the two groups.
Mansoor has claimed widespread backing among Taliban leaders based in Pakistan and on the battlefield, and took credit for the Taliban's brief capture of the northern city of Kunduz in September.