The military also said Thursday that it captured two suspected extremists they think are linked to the capture of three U.S. soldiers earlier this year.
It was not immediately clear if the U.S. raid on the splinter militia members would impact a six-month freeze on activities that the Mahdi Army leader - radical Shiite cleric Muqtada al-Sadr - called in August and has signaled in the past week he might extend.
In the past, al-Sadr has said that any Mahdi Army members who do not abide by his freeze would no longer be considered members of the militia. But he has also indicated that his fighters have the right to defend themselves if attacked by U.S. forces.
Al-Sadr's order to halt activities has been credited by American commanders as one reason why violence in Iraq has fallen dramatically in the past six months. However, it is unclear how much control al-Sadr maintains over his fighters as groups have splintered from the main movement.
Thursday's fighting took place in the early morning hours in Kut, 100 miles southeast of Baghdad, a local police officer said on condition of anonymity because he was not authorized to speak to the press.
The officer said eight militia members were killed; the U.S. military said in an e-mail to The Associated Press that it killed an "estimated" 11 fighters. The reason for the discrepancy was not immediately clear.
In a later statement, the U.S. military said the operation was targeting a suspect who was "reportedly responsible for attacks against Coalition forces."
Troops approaching the target were fired at with assault rifles and rocket propelled grenades, the military said. They then called in support aircraft. The local police official said at least two U.S. helicopters were used in the attack, along with an unknown number of fighter jets.
The military said no suspects were detained during the raid and that no U.S. troops were killed or wounded.
An official in al-Sadr's office in Kut described the U.S. action as "a criminal and cowardly attack by the Americans. They are trying to provoke people and ruin a stable security situation." He spoke on condition of anonymity as he was not authorized to speak to the press.
Despite the its freeze on activities, U.S. commanders have in the past said they would not stop targeting splinter elements of the Mahdi Army that they said continue to operate, despite al-Sadr's order.
In early October, U.S. forces killed 25 Shiite militia fighters in Khalis, north of Baghdad, who were believed to be part of a Mahdi Army splinter group.
In other developments:
Meanwhile, the military said it captured on Monday and Tuesday in Ramadi two suspects linked to the capture of three American soldiers taken during a May ambush near Youssifiyah, about 12 miles south of Baghdad.
The military said one of the suspects is thought to have "facilitated" the kidnapping and to have used his house to hide the soldiers. A weapon belonging to one of the U.S. soldiers was found at the residence of the other suspect.
Spc. Alex R. Jimenez and Pvt. Byron W. Fouty were seized May 12 when insurgents attacked and overran a checkpoint in the volatile area south of Baghdad known as the "triangle of death."
A third soldier, Pfc. Joseph Anzack Jr., was also captured during the raid, but his body was found May 23 floating in the Euphrates River. Four U.S. soldiers and an Iraqi soldier were killed during the ambush.
The Islamic State of Iraq, a front group for al Qaeda, claimed in an Internet video earlier this year that the three missing soldiers were killed and buried. The militants showed images of the military IDs of Jimenez and Fouty but offered no proof that they were dead.
Also Thursday, Sunni and Shiite lawmakers criticized a draft amnesty bill to release Iraqi detainees, saying it does not go far enough to release the innocent and is likely to be shelved when it goes before parliament. The measure was approved by Iraq's Cabinet the day before.
The measure will not be brought to parliament for debate until March at the earliest, said Sami al-Askari a key adviser to Prime Minister Nouri al-Maliki. Many key draft laws - including measures to share oil revenue and to allow some members of Saddam Hussein's Baath party to hold government jobs - have remained mired for months in Iraq's gridlocked parliament.
Both the Iraqi government and the U.S. military each hold more than 20,000 prisoners detained since the U.S.-led invasion of 2003.
Al-Askari, who is a parliament member, said the amnesty would not cover those convicted of terrorism, corruption, crimes against humanity and kidnapping.
The draft will also not involve prisoners being held by American forces, said Sadiq al-Rikabi, another al-Maliki adviser.
It was not clear how many prisoners might be affected by the proposed ban. Al-Askari estimated that "80 percent of those held in Iraqi prisons are there for terrorist crimes, therefore the amnesty would be for a limited number."
Falah Shanshal, a Shiite lawmaker allied to al-Sadr, said the bill was "useless" if it did not include prisoners in U.S. jails in Iraq. "It's not a general amnesty, and it will be useless," he said.
Sunni lawmaker Asmaa Adnan al-Dulaimi of the Iraq Accordance Front, the three-party alliance that has 44 parliamentary seats, told The Associated Press that the law "will hinder the release of many innocents" as it will encounter endless debate in parliament.
"The best thing is to leave this issue to the judicial system because it is the only side who can decide who is innocent and who is not," she said. "The judicial system should review the inmates' files carefully and immediately in order to have them freed and not stranded by the long political discussions."