On Tuesday, Iranian Foreign Ministry Spokesman Abbas Mousavi once again condemned the attack on the Iranian consulate building.
Tehran, he said, has also asked Baghdad to adopt more security measures to that effect.
In recent weeks, Iraqi cities, including Karbala, have been rocked by street protests over unemployment and a lack of basic services.
A group of so-called demonstrators scaled the concrete barriers surrounding the diplomatic complex in Karbala late on Sunday and spray-painted scurrilous writings on its perimeter walls.
Some other demonstrators also threw stones and burned tires around the Iranian consulate building, prompting Iraqi security forces to fire in the air to disperse the crowd.
Reports said no serious damage was inflicted on the diplomatic mission building and the Iranian staff and diplomatic employees were uninjured.
Iraq’s Ministry of Foreign Affairs on Monday condemned the attack on the Iranian consulate in Karbala, reaffirming Baghdad’s commitment to protection of diplomatic missions in the Arab country.
“The Ministry of Foreign Affairs condemns the attack by some demonstrators on the Consulate General of the Islamic Republic of Iran in the holy city of Karbala, and reaffirms the ministry’s commitment to the inviolability of diplomatic missions guaranteed by the Vienna Convention on Diplomatic Relations and the need not to endanger their security,” the ministry said in a statement.