Iranian authorities have arrested 35 people in relation to the 3 January attacks in the southeastern city of Kerman, the Intelligence Ministry has said, according to the semi-official Tasnim news agency.
The ministry said it had identified one of the two suicide bombers as a national of Tajikistan, who entered Iran illegally on 19 December.
More information will be released at a later date about the second suicide bomber, the ministry said, adding that the arrests had been carried out in several Iranian provinces.
The Islamic State claimed responsibility on 4 January for the attack that killed nearly 100 people and wounded 284, at a memorial to mark the fourth anniversary of top commander Qassem Soleimani's death in a US drone strike in Baghdad.
Tehran has vowed revenge for the bloodiest such attack since the 1979 Islamic Revolution.
"A very strong retaliation will be meted out to them by the hands of the soldiers of Soleimani," Iran's First Vice President Mohammad Mokhber told reporters in Kerman.
