In his message, Mokhber said, “I would like to extended condolences to the Russian government and people”.
Mokhber added that terrorism and the killing of innocent citizens is deplorable wherever it happens.
He noted that any government or group that commits such crimes or sponsors them must be prosecuted.
The Iranian first vice president also urged both Iran and Russia to further strengthen their determination to fight terrorism.
The terror attack on the Crocus Crocus City Hall concert venue outside Moscow has left more than 130 people dead and 150 others injured.
Daesh terrorist group has claimed responsibility for the attack.