Large explosions were heard late Wednesday in the center of Najaf, and residents said US forces appeared to be making an armed incursion into the Shi'ite holy city.
At least one civilian was killed and another was wounded, Iraqi authorities said.
Militant cleric Muqtada al-Sadr has been holed up in Najaf since early April, when he launched his rebellion against the US-led coalition with his armed militia.
American forces have been pressuring al-Sadr but have avoided a major assault for fear of damaging the Imam Ali shrine, which would inflame passions in the majority Shiite community.
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Skirmishes continued through the night, witnesses said, and a comprehensive casualty toll could not be obtained.