Coalition forces conducted two separate raids targeting suspected secret cell terrorists during pre-dawn hours Saturday in Sadr City," the statement said.
"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.
Seventeen more people were detained, it said.
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.
"Everyone who got shot was shooting at US troops at the time," said Lt. Col. Christopher Garver, "it was an intense firefight".
Residents said US attack helicopters fired missiles at targets in the densely-populated area of two million people in northeastern Baghdad.
"At about 4am, a big American convoy with tanks came and began to open fire on houses," said Bashir Ahmed, who lives in Sadr City's Habibya district. "We didn't even retaliate, there was no resistance."
"We are being hit while we are peacefully sleeping in our houses. Is that fair?", asked another woman as she watched a funeral procession in the Orfali district of Sadr City.
Several houses and shops, including a bakery were damaged by the tank fire while the civilian casualties included three members of one family according to Iraqi officials.
They also said several women and children, along with two policemen, were among those injured.
Sadr City is the stronghold of Moqtada al-Sadr, a Shia leader who wants US forces to leave Iraq.
Sheikh Salah al-Obaidi, a spokesman for al-Sadr condemned the raids: "The bombing only hurt innocent civilians," he said.
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.
US troops have also discovered a mass grave containing as many as 40 bodies near Fallujah in western Iraq.
A statement said that military officials are now investigating and confirmed many of the dead had gunshot wounds and had their limbs bound.