The clashes broke out when American tanks and troops moved into Kufa for the first time in an effort to weaken the militia of Muqtada al-Sadr, who launched an uprising against the coalition in early April. The fiercely anti-U.S. cleric routinely delivers a sermon at Friday prayers in Kufa.
U.S. forces fought militiamen near Kufa's Sahla mosque and an Iraqi counterterrorism force then entered and "cleared" it, the military said in a statement. Soldiers seized a machine gun, two mortar tubes and over 200 mortar rounds as well as rocket-propelled grenade launchers and rounds, it said.
Radhi Mohammed, a mosque employee, said American troops smashed the door with an armored vehicle and killed people inside. An Associated Press photographer saw bloodstains on the floor that indicated someone had been dragged for at least 10 yards. There was blood in the bathrooms.
Maj. Gen. Martin Dempsey, commander of the 1st Armored Division, said U.S. forces had taken care not to damage Shiite Muslim shrines even though militiamen were using them as fighting positions.
"We have no intention of entering the shrines," Dempsey said, adding that Iraqi security forces would enter them if necessary. The radical cleric's supporters have accused the military of desecrating holy places.
In other developments:
American troops also fought al-Sadr's militia, known as the al-Mahdi Army, around Kufa's technical college and a building known as Saddam's Palace, the military said. Thirty-two militiamen died.
Medic Maytham Lazim of the city's Furat al-Awsat hospital said 18 people were killed. Eleven others were injured. No U.S. casualties were reported.
Resident Mohammed Abdul-Kareem said the dead included three civilians whose houses were damaged in the fighting, which lasted from 10 p.m. Saturday until 6 a.m. Sunday.
In Karbala, no al-Sadr fighters or American forces were seen on the streets on Sunday, but the U.S. military denied claims by al-Sadr's office that all combatants had agreed to withdraw from the city.
"There was no cease fire, no deal made in Karbala," said Maj. David Gercken, spokesman for the 1st Armored Division. "We do not and will not make deals with militias or criminals."
U.S. forces captured 10 militia overnight in Karbala, but encountered little or no resistance during patrols, Gercken said.
"We have kept pressure on them, kept engaging them and been successful with those operations," Gercken said.
Iraqi leaders in Karbala had been trying to negotiate an end to the fighting, though coalition officials have demanded that al-Sadr disband his militia and "face justice." The cleric is wanted in the murder of a rival moderate cleric last year.
"There is no presence of armed militias in the city," said Adham Mahmoud, a hotel worker in Karbala said. "People have started leaving their homes and going into the streets. Some have started rebuilding their damaged houses."
No insurgents were seen around Karbala's Imam Hussein shrine, one of Shia Islam's holiest sites, but it was guarded by a special security force in civilian clothing that was appointed by top Shiite clerics.
"Iraqi security forces are already patrolling the city," the U.S. military said in a statement.
Gunmen killed a police captain and a university student in Baqouba, north of Baghdad, on Sunday, a hospital official said. Capt. Haidar Hadi was giving the student a lift to Baghdad when the gunmen opened fire. A police sergeant in the car was injured, said Nassir Jawad of Baqouba General Hospital.
Also Sunday, a policeman was killed and two others were seriously injured when a bomb exploded as they patrolled between Basra and Zubeir in southern Iraq, police said.
Insurgents routinely target police and other Iraqis who are working with the U.S.-led coalition governing Iraq.
In Basra, a mortar shell landed on a house in al-Iskan district, killing one woman and injuring five men, said Khalid Abdelallah, an official at Mawanei Hospital. It was unclear who fired the mortar round.