U.S. forces urged civilians to evacuate Tuesday and warned the militiamen they would be killed if they did not leave Najaf.
U.S. and Iraqi security forces also fought the cleric's loyalists in Baghdad's Sadr City neighborhood.
Late Tuesday, the Iraqi government vowed to crush the militants and urged them to take advantage of a limited amnesty and put down their weapons.
In other developments, Iraqi authorities ordered the party of politician Ahmad Chalabi to evacuate its Baghdad headquarters. An Iraqi judge has issued arrest warrants for Mr. Chalabi and his nephew for charges they say are politically motivated.