A fierce gun battle broke out after a joint US-Iraqi force arrested a rogue Shiite militia leader in Karbala, leading to an air strike and the deaths of some 17 militants, the military said.
US troops also on Friday captured four militants suspected of links to networks that smuggle weapons and fighters from Iran, which Washington accuses of fueling the violence in Iraq with its support of Shiite militias.
The US military has promised to crack down on Shiite militias, which have been blamed for thousands of execution-style killings and roadside bombings, as well as on Sunni extremists usually blamed for suicide attacks and other bombings.
Militia violence declined after radical Shiite cleric Muqtada al-Sadr ordered his fighters to lay low when a US-Iraqi security crackdown began in February. But such attacks have recently increased out of frustration over frequent raids against al-Sadr's supporters and the failure of security forces to stop bombings that target Shiites.