Iraqi officials, who spoke on condition of anonymity because they were not authorised to release the information, said eight civilians were killed and 44 others wounded in fighting in the Sadr City.
One seriously wounded man died as an ambulance carrying him to the hospital was caught in the crossfire, police said.
The clashes, centered in Sadr City, which has a population of some 2.5 million people, have taken a heavy toll on civilians.
The US military insists it takes all possible precautions to avoid hurting innocent Iraqis.
Lieutenant General Lloyd Austin urged al-Sadr on Wednesday to halt attacks by his loyalists.
Austin, the number two commander of US forces in Iraq, told reporters in Baghdad: "We hope that Muqtada al-Sadr will influence his elements to stop violence and that he will work in favour of peace."
Al-Sadr has warned of "open war" if assaults against his Mahdi Army, who were ordered by the cleric last August to observe a ceasefire, are not halted.
Austin blamed much of the violence on "Special Groups", fighters the US military says are renegade Mahdi Army elements trained by Iranians in the use of sophisticated weaponry.
"Special Groups criminals are continuing to hurt people with violent actions. They must be brought to justice. The people of Sadr City are tired of them," he said