Police say 60 Taliban killed in strikes, army says 11
The Nato-led force meanwhile rejected claims by the Afghan police and defence ministry that it was involved.
The separate US-led coalition that also carries out anti-Taliban operations was not available to comment.
Confusion about operations and death tolls is not uncommon, with the various military groups tasked with hunting down the militants blamed for destabilising Afghanistan often issuing different accounts of events.
"Sixty Taliban militants were killed in a Nato-led aerial operation last night on a Taliban gathering point in Zahri district of Kandahar province," provincial police chief Esmatullah Alizai said.
The strikes targeted a meeting of Taliban fighters late Monday and were followed by ground troops who entered villages in the province on Tuesday, Alizai said.
The dead included three well-known Taliban commanders, he said.
Zahri, about 30 kilometres east of Kandahar city, has been a flashpoint for Taliban violence and is close to where the militant movement was born in the early 1990s.
However, the Afghan defence ministry said only 11 militants were killed, according to its reports.
"In the joint Afghan National Army and Nato forces military operation 11 terrorists were killed in Nato air strikes," it said in a statement.