Shia militiamen fired several mortar shells at a US base in Najaf early yesterday and at a city hall guarded by Bulgarian troops in another Shia city. Elsewhere, four US soldiers died after their Humvee overturned during a combat patrol, the US Army said.

The sporadic overnight shelling of the US base in Najaf followed intense attacks Monday by militiamen loyal to radical cleric Muqtada al-Sadr, who pounded the base with mortars and fired rifles and machine guns. No US soldiers were killed in either attack. US officers estimate about 20 Iraqis were killed by US retaliatory fire.

In Karbala, 50 miles north of Najaf, the city hall and the police headquarters, which are guarded by Bulaarian soldiers, came under mortar fire before dawn Tuesday, Bulgarian Defense Ministry spokeswoman Rumyana Strugareva said.

No casualties or damage were reported after that attack which lasted about ten minutes. Sadr's forces have battled coalition troops since the occupation authorities sought his arrest last month for the killing of a rival cleric last year.

North of Baghdad, four US soldiers of the 1st Infantry Division died from injuries sustained when their vehicle rolled over Monday night during a patrol near Khalis, some 40 miles northeast of Baghdad, the military said in a statement.

At least 759 US troops have died in Iraq since the war began in March 2003.

In Najaf, US commanders said they are holding back fire to avoid serious clashes in the city, which is home to one of the most holy Shia Muslim shrines.

"I think every soldier here understands the sensitivities of the situation," said Lt. Col. Pat White. He added that US troops would "maintain our defense posture" until someone "much, much higher than me makes a different decision."

The yesterday's shelling was light compared to Monday's sharp clashes.

White estimated that 20 militiamen were killed in the Monday battle - based on bodies and "watching young men fall after being hit." He said there were few civilian casualties because troops were using precision fire.