The message purportedly from Hafez Saeed was posted to an IS website two days after the Afghan intelligence agency said he had been killed.
The audio could not be independently verified.
Saeed, a Pakistani, was reportedly killed in the Achin district of Nangarhar province late on Friday, the intelligence agency said.
Saeed switched allegiance last year from the Taliban to Islamic State in Afghanistan.
Islamic State figures have been targets for U.S drone strikes, which killed three other IS commanders in the same area in a week, including Shahidullah Shahid and Gul Zaman.
After pushing out the Taliban insurgents, Islamic State fighters have in the past two months gained ground in several districts of Nangarhar province, which shares a long and porous border with lawless areas inside Pakistan.
Achin fell to the IS militants last month after heavy clashes with the Taliban. – Reuters