Tanks, ground troops and aircraft have launched a major offensive against Iraqi Shi'ite militia, killing about 20 in a raid on a mosque in Kufa and attacking other positions around Najaf.
The fiercest fighting in the area for weeks killed at least 34 people and injured dozens, including civilians, overnight.
US commanders say they are trying to avoid inflaming religious passions but will attack mosques used in combat.
Moqtada al-Sadr has irritated the Shi'ite establishment by the use of holy places in his revolt.
Some Shi'ite leaders have also demanded the Americans show restraint in the shrine cities.
