Lieutenant-General Justin Cole, a US military spokesman, acknowledged in an email that aircraft were used.
A police source said the raids came after a US vehicle was targeted by a roadside bomb.
"Iraq is still under foreign occupation and Iraqis continue to die in great numbers"
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James Bays, Al Jazeera's correspondent in Baghdad, said a television cameraman had filmed bodies of dead children.
Several houses and stores were damaged.
Clouds of black smoke rose from the area early on Sunday as sirens wailed, heavy gunfire echoed and US helicopters circled overhead, Reuters television footage showed.
Relatives gathered at the Imam Ali hospital as the emergency room was overwhelmed with bloodied victims and the dead were placed in caskets covered by Iraqi flags.
The US military said "an estimated 49 criminals" were killed in three separate engagements during a raid targeting a suspected rogue Shia militia leader specialising in kidnapping operations for which he sought funding from Iran.
US troops returned fire after coming under sustained attack from automatic weapons and rocket-propelled grenades from nearby buildings as they began to raid a series of buildings in the district, according to a statement.
It said about 33 fighters were killed in the clash. Ground forces then called in air strikes, which killed some six fighters.
Sadr City is the main stronghold in Baghdad for the al-Mahdi Army, a Shia militia loyal to Muqtada al-Sadr, a Shia leader who has repeatedly called for US forces to leave Iraq.
The area has witnessed frequent clashes between US forces and fighters.
Priests set free
|Mourners chant slogans during funerals of|
the victims of the Sadr City attack [Reuters]
Also on Sunday, a Vatican spokesman confirmed that two Catholic priests, kidnapped in the northern city of Mosul, had been freed.
"I can confirm that they are free," the spokesman said.
Fathers Pius Affas and Mazen Ishoa had been kidnapped last Saturday after being threatened by an unknown group.
They are now back at their church in Mosul and well, church negotiators told AFP on condition of anonymity.
A day after the abductions, Pope Benedict XVI issued a plea from the Vatican for their release.