(Updates with official saying no one hurt)
BAGHDAD, April 21 A missile struck the central Baghdad headquarters of the Supreme Islamic Iraqi Council on Monday, said an official for the party, which is the main rival of cleric Moqtada al-Sadr for control of Shi'ite areas.
The official, whose party is the biggest Shi'ite group in the government of Prime Minister Nuri al-Maliki, later said that no-one was reported hurt.
Sadr's Mehdi Army fighters have launched missile and mortar strikes across Baghdad since Maliki ordered a crackdown on them a month ago.
Many of those missiles and mortar bombs have struck the Green Zone fortified government and diplomatic compound on the west bank of the Tigris river.
The Council's office is in the Karrada neighbourhood in the centre on the opposite bank. (Reporting by Peter Graff; Editing by Jon Boyle)