The militia, armed with a variety of weapons and some 30 vehicles, mounted an attacked on the offices of Ayatollah Seyyed Mahmoud al-Hassani that had its own armed guards at 11 pm on Wednesday and fighting continued until the early hours of Thursday, the television channel ash-Sharqieh reported on Thursday.
Several fighters were killed or injured in the course of the clashes and at least two of the attackers vehicles were left charred at the scene of the fighting.
Last Friday, a bomb went off in Ayatollah al-Hassanis office in the holy city of Karbala.
No one was injured in that attack.
Ayatollah al-Hassani is an outspoken critic of Iranian meddling in Iraq and has called for Irans embassy in Baghdad to be closed.
In June, his supporters held a protest outside the Iranian consulate in Karbala and torched Iran’s consulate in the southern Iraqi city of Basra.
They were protesting against a program aired on Irans state-run satellite channel al-Kowthar against the Shiite cleric.
Iran has at least seven Arabic-language television stations and more than two dozens journals spreading its propaganda in Iraq.