As many as 50 militiamen may have been killed in overnight and pre-dawn fighting in a cemetery in the Iraqi holy city of Najaf.
30 people were also believed to have been injured.
In the Baghdad suburb of Sadr City just under 20 militiamen, who support the cleric Moqtada al-Sadr, were killed.
US-led forces have been battling the militia in Sadr City, Najaf and Kufa, and Karbala where the fighting has largely died down after several tense weeks.
The US authorities want to arrest Mr al-Sadr in connection with the murder of another cleric and are trying to end his rebellion before an Iraqi government formally takes over sovereignty on 30 June.
In Baghdad, three Iraqis were killed and 11 injured in two separate roadside bomb attacks, one in the southwest of the city and one at the Jumhuriya bridge in the centre.
And three Iraqis were killed and 18 others, including a senior police officer, were injured in a car bomb explosion at Balad Ruz, 75km northeast of Baghdad, while the police chief of nearby Al-Khalis, who was injured in an assassination attempt on Monday, has died in hospital.
Russian company pulls out after more deaths
Two employees of a Russian energy company working on a power plant in Iraq were killed when gunmen opened fire on a bus transferring them to more secure quarters.
The firm, Interenergoservis, whose workers have been abducted and killed in previous attacks, is now withdrawing its remaining 234 employees from the country.
The bus was attacked by gunmen firing from two cars at the entrance to Dora power station on the southern outskirts of Baghdad.
Two Iraqis, described by Russian media as the bus driver and a guard, were also killed in the attack.
Two Russian engineers working for Interenergoservis were held captive for about a week this month after their car was ambushed. One of their colleagues was shot dead.
Eight employees were also held and released last month.
