An aide to the spiritual leader of Iraq's Shia Muslims, Ayatollah Ali al-Sistani, has called for an end to the fighting in the holy city of Najaf.
The militia have vowed to resist the American troops
American tanks went into the city's ancient cemetery in response to what US forces said were attacks by supporters of radical Shia cleric Moqtada Sadr.
It is not known how many people died in the fighting, but one source told the BBC that bodies littered the streets.
Sadr supporters have also attacked the US-led coalition's HQ in Nasiriya.
The Mehdi Army (MA) militants have pinned down foreign and other staff inside the building in the southern city.
Reports say they have also gained control of several strategic points in Nasiriya, including a central bridge.
There has also been fighting in the holy city of Karbala, where at least four Iraqis are said to have been killed.
Fears for holy sites
Heavy fighting in Najaf raged up until Friday afternoon when a pause set in but sporadic gunfire returned after dark.
Mr Sadr's followers showed off four holes in the golden dome of the Imam Ali mosque, one of Shia Islam's holiest sites, accusing the Americans of shelling it.
However, Brig Gen Mark Kimmit, the coalition's deputy operations director, suggested the cleric's own militia may have been responsible for the holes.
"I can just tell you by the looks of where we were firing and where Moqtada's militia was firing, I would put my money that Moqtada caused it," he said.
The BBC's David Willis in Baghdad says the Americans have consistently said they will not encroach on the Imam Ali Shrine but in recent days they have said their patience is wearing thin.
Mr Sadr, who is wanted by the US in connection with the assassination of a rival Shia cleric, launched an uprising against coalition forces last month.
Ayatollah Mohammad Baqer al-Mohri, aide to Ayatollah Sistani, called on both the US military and Mr Sadr's forces to leave Najaf.
He told Reuters news agency that the fighting was spreading fast and he feared for the holy sites and Ayatollah Sistani's safety.
US troops fired cannon and machine-guns at Shia militants sheltering in the sprawling cemetery, about three kilometres (two miles) from the Imam Ali Shrine, close to where Mr Sadr has taken sanctuary.
And American tanks blocked off roads between Najaf and the nearby holy city of Kufa, in an apparent attempt to prevent Mr Sadr from reaching Kufa for his habitual Friday prayers.
However, Mr Sadr appeared in Kufa to deliver his sermon in which he denounced coalition leaders and condemned Iraqis working for the occupying forces.
In Baghdad's mainly Shia slum of Sadr City, representatives of Mr Sadr urged young men to go to Najaf and join the fight and there were similar militant calls in Iraq's second city, Basra.