In a statement, the militant group said two members detonated explosive belts in the southeastern city of Kerman on Wednesday.
Crowds had gathered there to commemorate the death of top commander Qassem Soleimani, who was killed in 2020 by a U.S. drone strike.
Tehran had earlier blamed the blasts on "terrorists" and vowed revenge for the bloodiest attacks in Iran since the 1979 revolution.
"A very strong retaliation will be handed to them," First Vice President Mohammad Mokhber warned.
Similar condemnations came from President Ebraham Raisi and the powerful Revolutionary Guards, as well the top authority, Supreme Leader Ayatollah Khameini.
With the evidence of the previous day's carnage still fresh in the streets of Kerman...
the U.N. Security Council condemned what it called a "cowardly terrorist attack."
Islamic State has claimed responsibility for other attacks in Iran in the past...
including an attack on a shrine in 2022 which killed 15 people...
and twin bombings in 2017 targeting the country's parliament and tomb of the Islamic Republic's founder.
Authorities have called for mass protests on Friday.
That's when -- according to state media reports -- funerals for the victims are set to take place.
