"It is believed that the suspected terrorists have close ties to Iranian terror networks and are responsible for facilitating the flow of lethal aid into Iraq."
The statement said US soldiers faced "significant" resistance during the pre-dawn raids, including roadside bomb attacks as well as fire from rocket-propelled grenades and light weapons.
There were no US or Iraqi casualties, it said.
Residents said US attack helicopters fired missiles at targets in the densely-populated area of two million people in northeastern Baghdad.
Sadr City is the stronghold of Moqtada al-Sadr, a Shia leader who wants US forces to leave Iraq.
The US military also confirmed on Saturday that two of its soldiers have been charged with the premeditated murder of three Iraqis between April and June.
Michael Hensley, a staff sergeant, and Jorge Sandoval, a specialist, are accused of killing three Iraqis in separate incidents, then planting weapons on the victims' remains, the military said in a statement on Saturday.
Fellow soldiers reported the alleged crimes, which took place between April and the month of June in the vicinity of Iskandariyah, 50km south of Baghdad, it said.
Hensley is charged with three counts each of premeditated murder, obstructing justice and wrongfully placing weapons with the remains of deceased Iraqis, the military said.
He was placed in military confinement in Kuwait on Thursday.
Sandoval faces one count each of premeditated murder and placing a weapon with the remains of a dead Iraqi, a statement said. He was taken into custody on Tuesday while at home in Texas, and was transferred to military confinement in Kuwait three days later, it said.
In other violence in Iraq on saturday at least 16 people were killed in a suicide attack targeting a crowd of police recruits in Muqdadiyah, a market area 90 km north of the Iraqi capital Baghdad, police said on Saturday .
The bomber detonated his explosives belt outside a police station, a police officer said, confirming that all the victims were new police recruits.