Smoke was seen rising from Najaf before an expected major US-led assault on Shia leader Muqtada al-Sadr's al-Mahdi Army militiamen.
"Three US soldiers attached to the 11th Marine Expeditionary Unit were killed as a result of enemy action in Najaf province 15 August," said a US military statement on Monday.
Mortars later fell near Najaf police headquarters at around 8:00pm (16:00 GMT), while the clinic in the shrine said eight people were wounded on the second day of isolated clashes.
Bullets have also hit the northern wall of the Imam Ali shrine, witnesses said.
Meanwhile, at least 50 delegates from the key Iraqi National Conference in Baghdad prepared to drive to Najaf, hoping to persuade al-Sadr to withdraw his fighters from there and turn his al-Mahdi Army into a political party.
The delegation were due to travel on Monday but the trip was postponed at the last minute to Tuesday.
Conference backs talks
Participants had approved the proposal put forward by a relative of al-Sadr, Baghdad Shia cleric Shaikh Husayn al-Sadr.
He told the conference on Monday: "There are inviolable conditions in civilised countries, particularly that there is no place for armed militias."
Conference delegates have voted
for negotiations with al-Sadr
"I suggest you appeal urgently to Muqtada al-Sadr as we did yesterday to the Iraqi government and draw up a three-point resolution that everyone can agree with.
"Firstly, that the al-Mahdi Army withdraw from the shrine, that [they] renounce weapons and become a political party," he added.
Khudair al-Abbas, from the large Shia Dawa party of Vice President Ibrahim al-Jaafari, said his members fully supported the initiative.
In Najaf, a spokesman for al-Sadr, Shaikh Ahmad al-Shaibani, said the question of the militia laying down arms and becoming a political organisation could only be solved by "negotiations and not a unilateral decision".
Intermittent fighting broke out in Najaf on Sunday after a two-day truce - following a week of clashes - ended with the breakdown of negotiations between al-Sadr and the Iraqi government.
"A major assault by forces will be launched quickly to bring the Najaf fight to an end," Interior Ministry spokesman Sabah Kadhim said late on Sunday.
Muqtada al-Sadr has called on US
troops to leave the country
"This matter has to be brought to conclusion as fast as possible and we want to bring the situation to normalcy soon," he added.
Also on Sunday, foreign and Iraqi journalists and cameramen were ordered out of Najaf by local police, as authorities said their safety could not be guaranteed.
One person was killed and two wounded when US troops fired on pro-Sadr demonstrators near the cemetery, a surgeon said on Sunday.
The al-Mahdi Army is in control of the mausoleum of Imam Ali - one of the holiest sites for Shia Muslims - in the centre of the old city, and parts of a vast cemetery nearby.