Sayyid Badr Albusaidi and Amirabdollahian spoke on the phone on Thursday.
The Omani minister conveyed the message of condolence by Sultan Haitham bin Tariq Al Said to the people and government of Iran, as well as the families of the victims of the attack.
The Omani Foreign Ministry had already condemned the attack in a statement on its website.
The carnage left 15 people dead, including two children, as a gunman opened fire at pilgrims gathering in Shah Cheragh holy shrine.
The Daesh terror group claimed responsibility.