Sounds of heavy gunfire and explosions rattled the Al-Sadr City neighborhood from about 1 a.m. local time.
Iraqi government television says U.S. aircraft were attacking buildings in the area.
The U.S. military said the fighting started when U.S. and Iraqi forces raided the area to capture extremists suspected of operating torture chambers.
The police chief of Al-Sadr City, Hassan Chalub, said three civilians were killed and several others wounded in the fighting. He said several cars and houses were destroyed.
Iraq's Defense Ministry says U.S. troop reinforcements are arriving in Baghdad from Mosul in a bid to quell sectarian violence.
Also, the U.S. military today said three U.S. troops were killed by a roadside bomb blast southwest of Baghdad on August 6.
Insurgents also killed six Iraqi troops and wounded about 15 others today at a checkpoint near the northern Iraqi town of Ba'qubah.
(compiled from agency reports)
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