The Iranian statement comes amid ongoing demonstrations in Iraq against government corruption, and a rejection of Iranian involvement in the country's affairs.
On Thursday, 13 protesters were killed in the city of Nasariyah with 75 people injured, a security official and a medic told CNN on condition of anonymity, as they are not authorized to speak to the media. Authorities imposed a curfew on Nasariyah, which lies more than 200 miles southeast of Baghdad.
Iran's Foreign Ministry spokesman Abbas Mousavi expressed "hatred" for the rioters who stormed and torched the consulate on Wednesday. Mousavi called on the Iraqi government to deal with the "perpetrators of the attack responsibly, firmly and effectively," according to an Iranian foreign affairs ministry statement released on Thursday.
Iran's diplomatic staff evacuated the consulate before the attack, state-run Islamic Republic News Agency (IRNA) said Thursday. This is the second attack on an Iranian embassy in Iraq after its office in the Shia holy city of Karbala was attacked last month.
More than 300 people have been killed and 15,000 injured in Iraq since the start of anti-government protests on October 1.
Protests have erupted in Baghdad and in several Shiite provinces in the south over unemployment, alleged government corruption and a lack of basic services. Following the deadly government crackdown, however, protesters have demanded the government to step down and hold early elections under direct supervision of the United Nations, activists told CNN.