In a statement, the military said the raids targeted four cars belonging to "secret cell" networks believed to be "responsible for facilitating the flow" of weaponry from Iran to Iraqi militants.
The military said all victims were terrorists who attacked U.S. troops during the raid with rocket-propelled grenades. There were no U.S. casualties.
But news agencies quoting Iraqi officials and residents in the area reported that among the dead were civilians who were killed in their homes. They put the death toll at eight and say some 20 were injured.
An Al-Sadr City resident whose house had been damaged during the raid told Reuters: "I do not have sons. I live here with women, my two daughters. Why did they [U.S. forces] target my house? I do not know."
Al-Sadr City, Baghdad's largest Shi'ite neighborhood, is also the base of operations for the Imam Al-Mahdi Army, a militia loyal to radical Shi'ite cleric Muqtada al-Sadr. The fighters are blamed for being involved in sectarian killing in Baghdad.
In the Shi'ite holy city of Al-Najaf, a spokesman for al-Sadr condemned the raids. Sheikh Salah al-Obaidi was quoted by AP as saying, "The allegation that al-Mahdi Army members were the only ones targeted is baseless and wrong."
Links To Iran
Today's raids are the latest in a series of U.S. operations targeting militants in the area that U.S. commanders say receive weapons and support from neighboring Iran.
The military says the weapons have included sophisticated shaped explosives capable of penetrating U.S. armor.
In late May, the U.S. ambassador to Iraq and his Iranian counterpart met in Baghdad for landmark talks aimed at discussing ways to improve security in the war-torn country. Yet despite the four-hour talks, U.S. military officials say Iran has continued to foment unrest.
Tehran has repeatedly denied the charges and said it is in favor of a stable Iraq.
U.S. Soldiers Face Charges
In a separate development, the U.S. military said it had charged two of its soldiers for the murder of three Iraqis in different incidents south of Baghdad, between April and June 2007.
The soldiers are accused of murdering three Iraqis in separate incidents south of Baghdad, then planting weapons on the victims' remains.
The U.S. military identified the two as Staff Sergeant Michael A. Hensley and Specialist Jorge G. Sandoval.
Hensley is charged with three counts each of premeditated murder, obstructing justice, and "wrongfully placing weapons with the remains of deceased Iraqis."
Sandoval faces one count each of premeditated murder and placing a weapon with the remains of a dead Iraqi.
Both are in U.S. custody in Kuwait.
The charges were the latest to be leveled against U.S. troops in Iraq, including the killing by Marines of 24 unarmed Iraqis in the western Sunni city of Al-Haditha in 2005.
(with agency reports)