The intermittent fighting came as the military announced three US marines were killed "as a result of enemy action" in the province on Sunday.
Hundreds of demonstrators and tribal chiefs from across Iraq converged on the Imam Ali mausoleum, one of Shiite Islam's holiest sites, to protest at continued fighting between the militia and US-led Iraqi police in Najaf.
Dancing and singing, they brandished pictures of Sadr and denounced Iraq's interim Prime Minister Iyad Allawi and the US "occupying forces".
Mortars fell near the police headquarters at around 8:00 pm (1600 GMT), while the clinic in the shrine said eight people were wounded on the second day of isolated clashes since talks broke down between Sadr and the government on Saturday.
Iraqi officials have repeatedly insisted that the militia disarm and quit Najaf for there to be any peaceful solution to the crisis.
"A major assault by forces will be launched quickly to bring the Najaf fight to an end," interior ministry spokesman Sabah Kadhim said late Sunday.
Amid looming fears of a fresh offensive, police ordered all journalists out of Najaf on Sunday, as one person was killed and two wounded when US troops fired on pro-Sadr demonstrators near the cemetery, a surgeon said.
Bullets also hit the northern wall of the Imam Ali shrine, witnesses said. In Baghdad, at least 50 delegates from the national conference delayed plans to travel to Najaf until Tuesday morning, but voiced confidence they could persuade Sadr to vacate the shrine.
"We are hopeful and optimistic that we would be able to convince Sayed (honorific) Moqtada and his followers to leave the shrine," said Fadel al-Khorsan, an aide to cleric Sheikh Hussein al-Sadr, a relative of Moqtada.
"We are even ready to escort them to a safe place elsewhere in city and guarantee that no one will harm them in any way," he added as the second day of Iraq's national conference wound down.
The reaction in Najaf was muted.
"We can come to an agreement on this through negotiations. We are ready to defend ourselves as we are ready for peace," said Sadr spokesman, Sheikh Ahmed Shaibani.
Najaf police chief Ghaleb al-Jazairi said his elderly father in the southern city of Basra had been kidnapped by militiamen, aided by police who had defected to the Sadr's Mehdi Army, a week after his uncle was abducted.
Elsewhere, a teenage girl and her six-year-old brother were killed and four other relatives wounded when a mortar bomb aimed at a US base in Baquba hit their home, their father and the police said.
One Iraqi was killed and 17 others wounded when US tanks shelled neighbourhoods in Fallujah, a notorious Sunni insurgent bastion, a doctor said.
Further north, a top US commander threatened fresh assaults to wipe out insurgency in Samarra, two days after a deadly air and ground operation.
"If we find enemies in Samarra, we will strike, because it's good for people of Samarra and its good for people of Iraq," said Major General John Batiste, commander of the 1st Infantry Division.
In the southern city of Amara, one civilian was killed and two others wounded in afternoon clashes between Mehdi Army fighters and British troops, a doctor said.
A massive fire was still raging, one day after rocket-propelled grenades were fired at a nearby oil well, the head of Amara's civil defence force said.
"So far it has been impossible to extinguish the fire as this could only be done by using planes," said Lilu Saadun al-Muhamadawi.
London oil prices climbed to a new record high of 44.11 dollars a barrel as traders took fright at the persistent insecurity around Iraqi oil fields. In Nasiriyah, deputy governor Adnan al-Sharifi said a US journalist, Micah Garen, had been kidnapped while reporting on archaeological sites in the area.
Garen is the founder and head of Four Corners Media, a US firm specialising in film, photo and written documentaries, according to its website. Another two Turkish drivers were also reported abducted, as a Syrian and two Lebanese truckers were freed after a 10-day hostage ordeal, the mother of one of them told AFP.