Fighters loyal to radical cleric Muqtada al-Sadr pulled back and regrouped in alleyways north of Imam Hussein shrine, and U.S. soldiers were positioned west and south of the site. Smoke wafted over the golden dome of the shrine, apparently from a nearby a power generator that had been set afire.
Fighting also raged near the city's Imam Abbas shrine. American forces are concerned that any damage to the two shrines could enrage Iraq's majority Shiite population as the United States tries to stabilize Iraq ahead of a transition to sovereignty on June 30.
Insurgents fired two mortar rounds in central Baghdad on Thursday. The first fell near the office of the International Committee of the Red Cross, breaking glass in an adjacent building. The ICRC withdrew most foreign staff from Iraq after a deadly blast at its Baghdad headquarters last year.
Also Thursday, a rocket landed in a gas plant at the Dora oil refinery in Baghdad, injuring a worker and triggering a blaze that firefighters quickly extinguished. Dora is the biggest oil refinery in the capital.
On Wednesday, a bomb exploded beside a U.S. military convoy in Baghdad, killing one U.S. soldier and injuring another, the U.S. military said.
A total of 774 U.S. service members have died in Iraq since the beginning of military operations last year. Of those, 564 died as a result of hostile action and 210 died of non-hostile causes.
In other developments:
On Wednesday night, al-Sadr followers stormed three police stations in Najaf, killing one policemen and injuring two. The attackers looted several cars and some weapons, and destroyed computers and furniture, said Brig. Hassan Hamza, deputy police chief.
U.S. soldiers later arrived and retook the police stations.
Dozens of Iraqi police with assault rifles took up positions behind concrete barriers on the southern approaches to Karbala, possibly to prevent reinforcements from arriving to help militiamen in the city.
U.S. tanks, helicopters and jets attacked al-Sadr's fighters in Karbala on Wednesday, partially destroying a mosque that insurgents had used as a base. American forces killed 22 militants, and six coalition soldiers were wounded, U.S. Brig. Gen. Mark Kimmitt said in Baghdad. Four of the soldiers returned to duty.
Al-Sadr urged fighters in the city to resist American troops and compared their struggle to the Vietnam War.
Iraqi leaders in another holy city, Najaf, discussed how to peacefully resolve the confrontation between al-Sadr and the U.S.-led coalition that last month issued an arrest warrant against him in the murder of a rival cleric.
They have proposed that al-Sadr will end the standoff with American troops if the coalition postpones its legal case against him and establishes an Iraqi force to patrol the city. The deal would also require U.S. forces to pull out of the city and Kufa, and al-Sadr's militia to lay down its weapons.
Coalition officials have said they welcome efforts to work for a peaceful solution, even though they will not negotiate with the cleric and want him to face justice.
Half of the Mukhaiyam mosque in Karbala, a base for al-Sadr's followers, was destroyed and seven hotels were set ablaze in the fighting Wednesday. Most shops in Tal al-Zeinabiya, a central market, and three ambulances and two military vehicles also were destroyed.
"I appeal to the fighters and mujahedeen in Karbala to stand together so as none of our holy sites and cities are defiled. We are prepared for any American escalation and we expect one," al-Sadr said at a shrine in Najaf, where he is holed up.
"Let remind you of Vietnam," al-Sadr said. "We are an Iraqi people that has faith in God, and his prophet and his family. The means of victory that are available to us are much more than what the Vietnamese had. And, God willing, we shall be victorious."
It was the first time al-Sadr had appeared before reporters since his militia, Al-Mahdi Army, launched attacks on coalition troops in Baghdad and other cities in early April. He also condemned the abuse of Iraqi detainees by U.S. troops at Saddam Hussein's notorious Abu Ghraib prison.