Afghan intelligence said Hafiz Saeed was killed Friday in the Achin district of Nangarhar province. Achin was sacked last month by Saeed's fighters following intense battles with Taliban militants.
US drone strikes killed three other IS commanders in the same area in a week.
The audio recording posted on IS' Arabic website could not be independently verified and it was unclear from the content when it was recorded, Reuters reported.
The speaker on the tape said the IS movement's goal was to implement sharia Islamic law.
"We are ready to sacrifice our villages and homes," he said.
He also referenced battles between Taliban fighters and the new IS offshoots in Nangarhar, accusing some elements of the Taliban of selling out to neighboring Pakistan's powerful spy agency, Reuters reported.
— NDS Afghanistan (@NDSAfghanistan) July 11, 2015
"We are defending ourselves," he said.
Saeed is a Pakistani national and former Taliban commander who defected to IS last year.
After pushing out the Taliban insurgents, IS has recently gained ground in several districts of Nangarhar, which borders lawless areas of Pakistan, Reuters reported.
While Afghan officials said Saeed was one of approximately 30 suspected terrorists killed in a US drone strike Friday, American officials said they have no proof or confirmation that he was killed.
"Were there some leaders among those killed? Probably, but we have no confirmation" that Saeed is among the dead, a senior US military official told NBC News.
A senior member of the Afghan Taliban said that Saeed was known for his harsh policies and ruthlessness.
"In their clashes with the Afghan Taliban, he and his men had beheaded dozens of Taliban fighters. They did not even spare women in the fighting and ruthlessly beheaded them," he told NBC.