Heavy gunfire and huge explosions resounded Thursday as American forces battled Iraqi militiamen near a gold-domed shrine that is one of the most sacred sites for Shiite Muslims (search). Thick smoke rose over the city center.

The fighting continued during a surprise visit to Baghdad by Defense Secretary Donald H. Rumsfeld who was seeking to calm the storm over abuse of Iraqi prisoners by American soldiers. He was accompanied by Air Force Gen. Richard Myers, chairman of the Joint Chiefs of Staff, and some of the Pentagon's most senior lawyers.

Pentagon officials arranged meetings with the top U.S. commander in Iraq, Lt. Gen. Ricardo Sanchez, and other senior commanders.

In Karbala (search), fighters loyal to radical cleric Muqtada al-Sadr (search) regrouped in alleys north of Imam Hussein shrine. Smoke drifted over 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.

Imam Hussein was the son of the Shiites' most revered saint, Imam Ali Ibn Abu Talib, the Prophet Muhammad's cousin and son-in-law. Hussein was killed in a 7th century battle with the army of a Muslim Sunni leader, and Shiites view his death as the defining moment of their history.

Abbas, the namesake of Karbala's other prominent shrine, was a half brother of Hussein.

Residents said the fighting, which began Tuesday night, left many homes destroyed and shops gutted by fire, and many families fled to safer areas of the city. In some cases, men stayed while women and children left.

Young men gathered at some street corners to watch the fighting. Militiamen in groups of three and four moved in side streets.

Majeed Mohammed Ali, owner of a cloth shop across the road from the Imam Abbas shrine, and two employees loaded his merchandise into a truck for storage elsewhere.

"I cannot wait any longer. Many shops have been burned down. I will not reopen my shop until all this is over," Ali said from atop the truck.

Pilgrims pleaded with guards of the two shrines to let them in, but they remained closed. Many of the faithful searched for telephones to assure relatives that they were safe.

The U.S. military said a soldier was killed when a roadside bomb exploded beside his military convoy in Baghdad on Wednesday, and a U.S. Marine died of wounds suffered during security operations in western Anbar province on the same day.

The Marine was assigned to the 1st Marine Expeditionary Force which is based in Anbar, an area that includes Fallujah, Ramadi and other insurgency flashpoints.

As of Wednesday, 773 U.S. service members had died since the beginning of military operations in Iraq last year, according to the Defense Department. Of those, 563 died from hostile action and 210 died of non-hostile causes.

It was unclear whether the deaths reported Thursday were included in the Defense Department figures.

Insurgents fired two mortar rounds in central Baghdad on Thursday, injuring one Iraqi civilian.

Also Thursday, a rocket landed in a gas plant at the Dora oil refinery in Baghdad, injuring a worker and triggering a blaze that was quickly extinguished. Dora is the biggest oil refinery in the capital.

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.

Hospital officials in Najaf said four people were killed and six injured in overnight fighting between American forces and al-Sadr supporters.

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, Brig. Gen. Mark Kimmitt said in Baghdad.

Al-Sadr urged fighters in the city to resist American troops and compared their struggle to the Vietnam War.

Iraqi leaders in Najaf discussed how to peacefully resolve the confrontation between al-Sadr and the U.S.-led coalition that 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 al-Sadr and want him to face justice.

"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 Wednesday at a shrine in Najaf, where he is holed up.

It was the first time al-Sadr had appeared before reporters since his militia, Al-Mahdi Army, began attacking 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.