The latest incident in the run-up to 18 September elections claimed the life of Tor Mulla during a gun battle south of Deh Chopan in Afghanistan’s southern Zabul province on Friday.
A US military statement confirmed the deaths of a soldier and interpreter in a small-arms fire attack, but did not give names.
But a spokesman for the provincial governor, Gulab Shah Alikhail, confirmed the name of the Taliban commander, adding that the district in which he died was notoriously insecure.
Taliban spokesman Abd al-Latif Hakimi also said Mulla had been killed, as well as Mulla’s brother and wife. He claimed eight Afghan government soldiers had been shot in the fight.
US and Afghan government forces have mounted a series of operations in the south and east in recent months aimed at rooting out rebels before the elections.
The Taliban, ousted by US and opposition forces in 2001, have condemned the vote and claimed responsibility for attacks on several candidates.
Afghan and US officials say the rebels will not be allowed to disrupt polling.
In a separate incident, three Taliban rebels were killed when a bomb they were planting beside a road in Zabul province went off, Alikhail said.
Two Afghan government soldiers were killed in a clash in Helmand province on Thursday night, another Taliban hot spot in the south, an official in that province said.