The council's statement said the prosecutor's office has sent an information sheet and a special arrest warrant for Momika and requested Interpol to notify Baghdad should he be arrested.
The desecration and burning of the Quran in Stockholm has sparked a wave of condemnation across the world. Iraq has called on the Swedish authorities to extradite the immigrant responsible for the incident.
Many heads of state, along with the secretary general of the Arab League and the head of the Gulf Cooperation Council, have condemned the act.
A similar demonstration took place in Sweden in January when Danish far-right politician Rasmus Paludan burned the Muslim holy book in front of the Turkish embassy.