Hafiz Waheed, a successor to Abdul Rauf Khadim who died in a US drone strike last month, was killed along with nine others in the Sangin district of Helmand province yesterday, according to a defence ministry statement.
"All the militants were associated with Islamic State group," the statement said, adding that six others were wounded in the strike.
NATO forces, who remain in the country in a limited training mission, were not involved in the operation, a spokesman said.
Khadim, Waheed's uncle, was a former Taliban commander and Guantanamo detainee who allegedly changed his allegiance to IS, raising fears the jihadist group was seeking to expand its operations in Afghanistan following the end of NATO forces' 13-year combat mission at the end of 2014.
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But IS has never acknowledged having representatives in Afghanistan, and a senior Taliban commander told AFP on condition of anonymity that Khadim had "not formally joined IS and IS had not recognised him".
Afghan security officials have launched a major operation against insurgents in Helmand designed to weaken the Taliban before the start of the so-called "fighting season".