Reports said U.S. tanks advanced into the town and fought with militiamen near the main mosque for about two hours around midnight. Residents said the fighting was the most intense in the area in the past six weeks.
Clashes were also reported in the nearby city of Al-Najaf.
The fighting comes three days after Shi'a clerics who negotiated with al-Sadr said he had offered a truce. U.S. commanders said they were willing to hold their offensive for some time to see whether al-Sadr kept up his offer.
In Baghdad, meanwhile, U.S. and Iraqi representatives have postponed further negotiations over the selection of an Iraqi president to take over when the U.S. occupation transfers sovereignty to Iraqis on 30 June.
The two sides tentatively agreed on 28 May that Shi'a Muslim Iyad Allawi should fill the prime minister's post, but negotiations deadlocked after the U.S.-appointed Iraqi Governing Council effectively backed a presidential candidate despite U.S. pressure to hold off on such a decision.
Governing Council member Mahmud Uthman told Reuters that the United States wants the talks to resume tomorrow. Much of the debate is said to revolve around on two possible candidates, Adnan Pachachi and Ghazi Ajil al-Yawir, both of whom sit on the Iraqi Governing Council.