A medic at Al-Sadr hospital, one of the main medical facilities in the impoverished Shia district of some two million people, said seven bodies had been brought in.
The US military was not immediately available for comment.
Since March 25, US and Iraqi forces have been battling anti-government fighters, mostly those belonging to Shia leader Muqtada al-Sadr's Mahdi Army.
Hundreds of people have since been killed.