The bombings which began at around 2100 GMT on Tuesday, left 78 injured, medical sources told Aljazeera.
Clashes erupted between US forces and al-Mahdi Army fighters during the US raid and a US aircraft raked one area with heavy fire.
"Right now we are in there. We are fighting the terrorists so we can re-establish civil-military operations and get back to the reconstruction projects that the people of Sadr City want," said army spokesman Major Philip Smith.
One local resident said he counted up to two dozen US tanks and other armoured vehicles in the early hours of Wednesday on the streets in the western part of Sadr City.
Eliminating armed opposition
Fighters have established large swathes of control in the sprawling, poor neighbourhood to the northeast of Baghdad's city centre.
Al-Sadr's supporters are fighting
US-led forces across Iraq
The area is predominantly home to the city's Shia, many of whom are loyal to leader Muqtada al-Sadr whose al-Mahdi Army has been fighting US-led forces around the country.
US officials have said they intend to eliminate armed opposition to the Iraqi administration before elections planned for January.
Officials in Washington said on Tuesday the military was tapping emergency funds partly in anticipation of heavy fighting in the coming months.
Iraq's most influential Shia cleric has said a raid by US forces on the office of Muqtada al-Sadr in Najaf has contravened a peace deal negotiated last month to end fighting in the city.
Ayat Allah Ali al-Sistani's office said the raid on al-Sadr's office and the jailing of some of his followers this week, was inconsistent with the deal between the US-backed Iraqi government and al-Sadr, which al-Sistani negotiated.
Under the deal, US forces were
supposed to withdraw from Najaf
"This step is considered contrary to the peace initiative on whose basis the Najaf crisis was solved," a statement issued by al-Sistani's office in Najaf said.
"We think that there was no justification for a military step of this type. [Al-Sadr's] office had previously agreed on inspections by the Iraqi police and the matter was completed with ease," the statement dated 21 September read.
Al-Sistani returned to Iraq from surgery in England to negotiate the peace agreement between the US-backed Iraqi government and al-Sadr, whose fighters were holed up inside Najaf's Imam Ali mosque.
Hundreds died in weeks of fighting around the mosque.
Under al-Sistani's deal, US forces were supposed to withdraw from the city.