The US statement did not say whether US or Iraqi troops had been killed or wounded in the battle.
At least three of the dead were al-Mahdi army fighters, according to Razak al-Musawi, a local spokesman for the political movement of Shia leader, Muqtada al-Sadr.
"The Americans were looking for a well-known member of the Mahdi Army named Hamza Matrud. There were three people killed and seven wounded from the Mahdi Army," al-Musawi said.
The US military did not give any names, but said its target was a 100-member al-Mahdi army unit responsible for bomb and mortar attacks on US-led troops, civilians, and the assassination of two government officials.
Cities in south-central Iraq have seen several running battles in recent months between rival Shia fighters, US and Iraqi forces.