Witnesses said seven or eight US tanks surrounded the governor's house, about five km from the sensitive religious sites in the city centre, and troops took occasional fire from militiamen holed up in the area using AK-47s and rocket propelled grenades.
Six Iraqis, including a suicide bomber, and a US soldier were killed and 25 people wounded in a car bombing early on Thursday on a bridge outside the American headquarters here, a senior military officer told AFP.
Among the wounded were 23 Iraqis, including three policeman, and two soldiers, the officer said.
The military had earlier put the Iraqi wounded at 26.
The nationality of the bomber was not known.
US tanks also moved into nearby Kerbala, another city holy to Shia Muslims, about 100 km south-west of Baghdad. The tanks took up positions close to the main shrines after destroying Sadr offices with machinegun fire.
Najaf locals said some fleeing militiamen had taken refuge in their homes, raising fears US forces could be drawn into urban fighting if they decided to flush out militia in the area.
Doctors at a local hospital said they had received three dead from the area - two women and a nine-year-old child - and were also treating at least nine wounded, some of them women.
The troops retook the governor's office as Paul Bremer, the US-appointed administrator of Iraq, named a new governor for the city and again denounced Sadr as an outlaw.
A senior coalition military official said the governor's office had been taken largely without a fight.
But east of the city, across the Euphrates River, US forces drew out fighters of Sadr's Mehdi Army, and killed 41 of them in fierce fighting, the official said. He gave no details about any US casualties.
Lieutenant Colonel Pat White, head of the 2nd Battalion, 37th Armoured Brigade around the governor's mansion, said his force was still taking fire from areas around the building.
"In order to secure the governor's compound we are getting contact from all sides and we are dealing with it now. Looks like the enemy is now breaking contact," he told CNN.
As he was being interviewed, his voice was drowned out by gunfire, which he identified as being from a heavy machine gun on one of the tanks guarding the compound. "If you gonna go down in there, you'd better be prepared for it because there are a lot of them," he said, adding that his battalion had killed about 20 Mehdi Army fighters.
FIGHTING IN KERBALA: In Kerbala, witnesses said about eight heavy armoured vehicles and six lighter vehicles were positioned in the city centre, about 500 metres (yards) from the Imam Hussein and Imam Abbas shrines.
Witnesses earlier said US troops were engaging Mehdi Army fighters firing RPGs, AK-47s and mortar rounds near the city's centre.
Italian troops also clashed with Sadr's militiamen, engaging in a short gunbattle south of Nassiriya, Italian officials said.
US-led forces in Iraq are trying to crush Sadr's militia before a scheduled June 30 hand over of sovereignty to Iraqis. They have said they will refrain from entering Shia shrines in Najaf and Kerbala, which would incite widespread fury.
Mainstream Iraqi Shia leaders urged Sadr this week to disarm and allow a political end to his nearly month-long stand-off with occupying troops in and around Najaf.
Earlier, as the operation was launched, witnesses reported seeing plumes of smoke rising from a cemetery on the fringes of the city as US helicopters swooped low over the area.
Bremer, speaking to reporters as he appointed the new governor for Najaf, denounced Sadr, saying he had used the holy sites of the region - which are deeply sacred to Iraq's 60 percent Shia majority - to launch his rebellion.
"These armed bands have fired mortars from the mosque of Kufa, they have stored arms and munitions in the mosques of Iraq's holy cities," Bremer said as he installed Adnan Zurfi as Najaf's governor.
The Shia leaders called on Sadr to pull out of mosques in the area and Bremer suggested the US-led occupation would help them reassert control over Najaf and other cities held by rebels, without specifying how.
Bremer called on Sadr, who is wanted in connection with the murder of another Shia scholar last year, to surrender.