By EDWARD WONG and MARIA NEWMAN

The battles, which began on Thursday, were the most intense since the American military started an operation here Tuesday night to crush the militia of Moktada al-Sadr, the radical Shiite cleric who has sought refuge in the nearby city of Najaf and its nearby town of Kufa.

In other fighting, around the central holy city of Najaf today, American soldiers killed 12 of members of Mr. Sadr's militiamen, Brig. Gen. Mark Kimmitt, the chief military spokesman, said in Baghdad.

The fighting in Najaf came a day after American forces captured the governor's office there, and General Kimmitt said that the troops were trying to respect the reverence of the holy city in installing a new governor.

"We remain extraordinarily sensitive to the religious significance of the town of Najaf," he said. "This restoration of the governor's building for the new governor should not be interpreted as an offensive against the city of Najaf, but simply an opportunity to restore legitimate Iraqi control by the appointment of the government — the new governor — as well as the restoration of a place for him to operate out of."

The seizure of the governor's office was the most aggressive move yet by the American military in its effort to quell the rise of Mr. Sadr, who has led a monthlong resistance in Najaf and nearby holy cities.

Mr. Sadr emerged from hiding today to tell worshipers at a mosque in Kufa that he rejected President Bush's public apologies for the American mistreatment of Iraqi prisoners.

Mr. Bush's "apology isn't enough," The Associated Press quoted Mr. Sadr as saying. "This crime isn't tackled by an apology," he continued. "Those who did this crime should be punished the same way in the same place."

In Karbala, members of the militia, known as the Mahdi Army, attacked one American patrol after dark on Thursday and another this morning, resulting in firefights that lasted several hours.

In the first, soldiers killed at least five insurgents and wounded six, Maj. Mark Grabski of the First Armored Division said. Soldiers on patrol this morning killed at least 20 insurgents, Capt. Robert Adcock said.

A civilian riding by on a moped near the end of the clash today was accidentally shot by American soldiers and died, officials said, despite the efforts of an Army medic to save his life.

The fighting took place in a Karbala neighborhood less than a mile southwest of two of the holiest places of pilgrimage for Shiite Muslims, the golden-domed Shrine of Hussein and the ornate Shrine of Abbas. The American military has been careful not to encroach on the immediate area of the shrines to avoid inflaming Shiites across Iraq. Instead, commanders have been sending patrols through the troublesome neighborhood to draw fire from militiamen and then counterattack them.

"I think they had enough today," Captain Adcock said of the insurgents as he chewed on a cigar after today's fighting. "They may get ready and go back tonight. But right now they've had enough."

Soldiers first began moving into the neighborhood early Wednesday, and each patrol has met stubborn resistance. By this morning, the fighters had laid trunks of palm trees and large boulders across the neighborhood's main avenue in an effort to block the Americans' path. A dozen Bradley fighting vehicles and two armored personnel carriers rolled around the obstacles as more than 100 soldiers made their way on foot along the dun-colored buildings on either side.

The going was treacherous for fighters on both sides. Militiamen fired rocket-propelled grenades and AK-47 automatic rifles at the soldiers while ducking behind houses and racing down alleyways. The soldiers moved low along walls and inched their way down a milelong stretch of road, returning fire the entire time.

At one point, an American sniper killed an insurgent looking around the corner of an alley with a shot to the head. A rocket-propelled grenade whooshed past the faces of more than a dozen soldiers crouched against a wall. At least one Bradley fighting vehicle took a direct hit from an R.P.G., though no one inside was wounded.

One soldier fainted from heat exhaustion, and two were dragged into Bradleys and given water before they collapsed.

Roadside bombs exploded along the length of the street. Soldiers had to sprint past some that had not gone off. The Bradleys fired their 25-millimeter cannons at figures darting down alleyways, even as insurgents poked AK-47's around corners and sprayed the area.

By the time the last bullet was fired, bodies of Iraqi men lay strewn across the roads. One crouching in a bush had been killed by shrapnel from three grenades. Another, a man in a beige robe, writhed in a pool of his blood for a half-hour before falling still.

Back at Camp Lima, a Polish-controlled base that the Americans occupied last weekend, soldiers drained by the battle lay asleep in the sand next to their vehicles. They were on call, waiting for word on whether they would have to go out on patrol again in the evening.

Lt. Col. Gary Bishop said the troops would continue patrols and raids until they drove the Mahdi Army from the city. The goal is to put Iraqi security forces back in charge of Karbala and limit Mr. Sadr's circle of influence to Najaf, where, the colonel said, it is hoped that senior clerics will deal with him.

"The insurgents don't have the support of the people here," Colonel Bishop said. "They now know the local populace is working with us against them."

Some residents of Karbala expressed a more ambiguous view of the conflict. Many of the Mahdi Army fighters hail from the Sadr City slum in Baghdad, and people here and in Najaf generally want the Mahdi fighters to leave their cities. But those same residents often also regard the Americans as foreign invaders.

"We don't support either side," Ahmed Abbas, 24, a grocery store owner, said. `We don't want the Americans to kill the members of the Mahdi Army, but we also don't want the Mahdi Army to win."

Mr. Sadr emerges from hiding almost weekly to stoke the resentment to the American presence.

. Today, he had to evade American forces surrounding his home city of Najaf to reach the mosque in Kufa, six miles away, where he addressed the Friday worshipers. .

"What sort of freedom and democracy can we expect from you when you take such joy in torturing Iraqi prisoners?" Mr. Sadr said, referring to Americans, according to The A.P.

"America claims that it is fighting terrorism, and not sponsoring it, and is spreading justice and equality among peoples and freedom and democracy," Mr. Sadr said. "Now it is doing the same acts done by the small devil Saddam and in the same place where Iraqis were oppressed."

United States officials have asserted that the prisoner abuses were isolated and that six soldiers are facing criminal charges, with the possibility that more will be charged.

On Thursday in Washington, Mr. Bush told King Abdullah II of Jordan that he "was sorry for the humiliation suffered by the Iraqi prisoners and the humiliation suffered by their families."

Just south of Baghdad, a Polish and an Algerian journalist were killed in a drive-by shooting today in the latest deadly attack against reporters in Iraq, several news agencies reported.

Both victims worked for Poland's TVP television, where officials identified them as Waldemar Milewicz, one of Poland's star television reporters, and his Algerian picture editor, Mounir Bouamrane, The A.P. said.

More than two dozen journalists have been killed in Iraq since the war began in March 2003, according to the Committee to Protect Journalists.

Edward Wong reported from Karbala and Maria Newman contributed reporting from New York for this article.