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BAGHDAD, Iraq (CNN) -- Iraq's Defense Ministry sent reinforcements to the southern city of Diwaniya after weekend clashes between government troops and followers of a radical Shiite cleric left more than 60 dead, Iraqi and U.S. military officials said.
The deployment came as a U.S. commander said members of at least two brigades of Iraqi forces have refused orders to fight outside of their operating areas.
The Diwaniya fighting left 23 Iraqi soldiers and 38 militiamen dead, and 40 wounded, amid conflicting reports of how the clashes began.
The Defense Ministry said the fighting began late Sunday after a large number of gunmen attacked several police stations in the city, taking over many of them. Iraqi soldiers later clashed with those gunmen, the ministry said.
While clashes were going on in parts of the city, the ministry said, the Iraqi army had generally taken control of the situation, including recapturing the police stations that had fallen under control of the gunmen.
An Iraqi army official said the clashes erupted after Iraqi soldiers began searching various parts of Diwaniya, a stronghold of the Mehdi Army militia, which is loyal to Shiite cleric Muqtada al-Sadr.
But Deputy Prime Minister Barham Salih told CNN that al-Sadr's associates have said "these groups were operating outside his control."
He called the fighting in Diwaniya "important and significant," since it involved troops from a Shiite-dominated government taking on a Shiite militia.
"While one regrets the loss of life in the conflict today, one should also recognize this is a sign of leadership and seriousness by the government to take on those who violate the law," he said.
Diwaniya is more than 100 miles south of Baghdad.
Brig. Gen. Dana Pittard, the commander of the U.S.-led Iraqi Assistance Group, told reporters at the Pentagon that Iraqi troops and police held their ground in "tough fighting" against the Mehdi Army.
"The 8th Iraqi Army ... working closely with the Iraqi police, repelled the attacks of the insurgents," Pittard said.
Car bomb kills 11
Sunday's clashes in southern Iraq came as U.S. and Iraqi troops worked to roll back a wave of sectarian violence between Shiites and Sunnis and insurgent attacks in Baghdad that have left thousands of Iraqis dead in recent months.
Eight American troops were killed over the weekend, all but one of them in attacks in and around Baghdad on Sunday, the U.S. command in Baghdad reported.
The latest American deaths bring the number of U.S. troops killed in Iraq to 2,622. Seven American civilian contractors of the military also have died in the conflict.
At least 11 people were killed and 63 were wounded when a suicide car bomber detonated his explosives at an Iraqi police checkpoint near the Interior Ministry Monday morning, Baghdad emergency police said.
Maj. Gen. William Caldwell, a U.S. military spokesman, said the joint effort has reduced the number of killings, abductions and attacks reported so far in August. The number of car bombs dropped from 16 two weeks ago to eight last week, and he said Baghdad's murder rate is down by nearly half since July.
"However, as we know, the insurgents and terrorists are punching back," Caldwell said.
Thousands of additional American troops were sent to Baghdad to bolster security there. But they have yet to move into Sadr City, the Shiite district that is the base of al-Sadr's power.
Caldwell said the decision about whether to go into Sadr City would lie with Iraqi Prime Minister Nuri al-Maliki, whose ruling coalition includes lawmakers from al-Sadr's political party.
"His intent is for Iraqi security forces to operate throughout the entire city of Baghdad," Caldwell said.
Al-Sadr is the son of a prominent Shiite ayatollah killed during the rule of ousted Iraqi leader Saddam Hussein. He led two uprisings against U.S. troops in 2004.
Britain's defense secretary, meanwhile, said that security had improved in southern Iraq, Reuters reported. His Iraqi counterpart predicted that formal control of another province in the region, Dhi Qar province, would be handed back to Iraq soon. (Full story)
Some Iraqi forces refuse to deploy
About 100 soldiers from a unit in the 10th Iraqi Army, based in southern Iraq, refused to deploy to Baghdad to assist the joint operation there, Pittard said.
Pittard said he also knew of at least one other instance in which Iraqi forces refused to deploy when ordered.
"There was another case of the 2nd Battalion, 3rd Brigade of the 2nd Iraqi Army Division that was up in northern Iraq that was to go and deploy ... to Ramadi," Pittard said. "A number of the members of that unit ended up not deploying."
He did not say when or how many troops were involved in the second incident and could not say if any of the troops would be punished.
An investigation is still under way into the members from the 10th Iraqi Army Division, he said, though it appeared Iraqi commanders would not be deploying the unit anyway.
Pittard acknowledged that the deployment issue still needs to be tackled and the mindset of a national army must be instilled in the troops.
The problem undercuts what the United States is trying to do -- create an Army that will be able to deploy anywhere in the country and be a cohesive fighting force.
"For many of those soldiers, they just thought that they would be operating in their homeland areas," Pittard said.
Asked about statements from Iraqi senior leaders that Iraqi forces are ready to hold their own, he responded that he does not believe U.S. and coalition forces will be leaving soon.
"If your question is, should coalition forces leave in the next couple months, my answer is I think that's premature, based on what we see on the ground," Pittard said.
The Iranian ambassador in Baghdad, meanwhile, said Monday that Iran wants an active role in the rebuilding of Iraq, including the development of its military and intelligence services.
Ambassador Hassan Kazemi Qomi said Tehran is interested in having a stable Iraq on its western border, led by an independent government with popular support.
"When we say we are ready to help in all fields, it is natural that that includes the field of security," Qomi told CNN.
Lt. Gen. Robert Fry, the commander of British troops in southern Iraq, told reporters last week that Britain "can see a very clear Iranian role in stoking up violence inside Iraq." Iran has denied supporting insurgents. (Full story)
CNN's Mike Mount and Mohammed Tawfeeq contributed to this report.