A spokesman for Shia leader, Muqtada al-Sadr has reportedly said that US occupation forces provoked the clashes.
Shaikh Ahmad al-Shaibani told AFP that US soldiers at a base in Najaf, previously occupied by Spanish and Latin American troops, provoked clashes by firing at a pickup truck transporting fighters from al-Sadr's Mahdi army from Najaf to Kufa on a back street in the city's industrial neighbourhood.
Shaibani said this alleged attack on al-Sadr's men prompted them to fire mortars on the base and the checkpoint which was set up on the main road outside the base.
The fight that ensued killed four civilians and one Iraqi policeman, with doctors at Najaf's Hakim General Hospital saying late on Monday that there were at least two other people killed in their cars near the base, but it was too dangerous for emergency crew to retrieve them.
"America is responsible for the blood of innocent Iraqis," said Shaibani.
In Karbala, 80km north of Najaf, the city hall and police headquarters, which are guarded by Bulgarian soldiers, came under mortar fire before dawn on Tuesday.
Aljazeera's correspondent reports that armed clashes between supporters of al-Sadr and Polish troops as well as Iraqi police, occurred later.
No casualties were reported.
North of Baghdad, four US soldiers died from injuries sustained when their vehicle rolled over on Monday night during a patrol near Khalis, some 60km northeast of Baghdad, the occupation military said in a statement.