Separately, a group linked to al Qaeda claimed responsibility for Monday's car bomb assassination of the Iraqi Governing Council president in a statement posted on a militant Islamic Web site.
The head of the Monotheism and Jihad Group is believed to be Abu Musab al-Zarqawi, a Jordanian wanted by the United States in connection with numerous terrorist attacks. He is suspected of strong links to Osama bin Laden's network. It was the second group to claim responsibility.
In other developments:
As of Tuesday, May 18, 787 U.S. service members have died since the beginning of military operations in Iraq last year, according to the Department of Defense. Of those, 574 died as a result of hostile action and 213 died of non-hostile causes.
It was unclear whether the latest deaths were included in Tuesday's total.
In Karbala, the militia of cleric Muqtada al-Sadr was operating from the Imam Hussein shrine in the center of Karbala, said Cpt. Noel Gorospe, spokesman for the U.S. Army's 1st Armored Division.
The city south of Baghdad has been the scene of heavy fighting since al-Sadr launched an uprising against the U.S.-led coalition last month.
"They use mainly the windows of the second floor of the shrine," to fire at troops, Gorospe said at Camp Lima, a coalition base on the outskirts of Karbala. Insurgents were using small arms, mortars and rocket-propelled grenades, and their use of the shrine was more noticeable in the past three days, he said.
American troops and militiamen fought Wednesday near a militia checkpoint 100 yards from another holy site in Karbala, the Imam Abbas shrine, witnesses said.
The U.S. military confirmed there was fighting Wednesday, but did not say where.
An al-Sadr militiaman was killed overnight and six others were killed in fighting Wednesday morning, said hospital sources who requested anonymity.
Daily insurgent attacks have centered on Karbala's Mukhaiyam mosque and the surrounding area, which the U.S. military took over in operations last week. The coalition said Iraqi fighters had used the mosque as a military base, and said it had no intention of relinquishing the mosque until militias leave the town.
Gorospe said an AC-130 gunship was used in an airstrike against insurgents around the Imam Hussein shrine in recent days, but said it did not shoot into the shrine.
Since Tuesday, U.S. F-16 jets have been flying over Karbala around the clock.
Al-Sadr has accused U.S. forces of desecrating shrines in Karbala and another holy city, Najaf. The U.S. military denies the allegations, saying militiamen have used Muslim holy places as firing positions and storerooms for weapons.
Militiamen fired two mortar rounds at a U.S. convoy in Najaf on Wednesday, witnesses said. The shells missed their target, hitting a hotel and a residential building and injuring five civilians, including two boys.
On Tuesday, three civilians were killed and 11 injured in fighting in Najaf, said Hussein Hadi, deputy director of al-Hakim hospital. It wasn't clear which side was responsible.
About 300 Iraqis from Baghdad and other areas traveled Wednesday to Najaf to protest the alleged desecration of holy sites by U.S. forces. The group of mostly young men gathered outside the Imam Ali shrine, waving Iraqi flags and photos of al-Sadr.
The statement by the Monotheism and Jihad Group was the second Internet claim of responsibility for the killing of Governing Council chief Abdel-Zahraa Othman, better known by the name he had adopted in exile, Izzadine Saleem. A statement had been posted Monday by a previously unknown Iraqi group, the Arab Resistance Movement.
"Another lion of the lions of the Monotheism and Jihad Group leapt to seize a rotten head from among the heads that betrayed God and his prophet and those who sold their religion and lives to their American masters and those who are allied with them," it said.
The statement, whose authenticity could not be confirmed, said other members of the Iraqi Governing Council could meet the same fate.
The body of Saleem and those of six bodyguards and aides who died in the bombing arrived Wednesday in Najaf for burial. Draped in Iraqi flags, the coffins were taken to the Imam Ali shrine for prayers.
Brig. Gen. Mark Kimmitt, the chief military spokesman in Iraq, initially said the car bombing that killed Saleem had the "classic hallmarks" of al-Zarqawi. But Kimmitt later said another group may be to blame "because of methodology in some of the techniques that were used." Kimmitt did not elaborate.
On May 6, the Monotheism and Jihad Group issued a Web claim of responsibility for an attack on the U.S.-led coalition's headquarters in Baghdad that killed five Iraqi civilians and a U.S. soldier.
An earlier purported al-Zarqawi statement appeared on a Web site claiming responsibility for an April 24 suicide boat attack on Iraq's oil terminal in the Gulf that killed three American service members.