A rocket-propelled grenade attack killed the US soldier and wounded two others in the slum on Tuesday, US Lieutenant-Colonel James Hutton said.
Earlier, senior Health Ministry official Saad al-Amili said a total of 33 people were killed and 193 injured in the Sadr City clashes in the previous 24 hours.
Fifteen were killed and 67 wounded on Tuesday morning alone, he added.
Aljazeera later learnt that 41 people had died in the clashes.
Residents said loud explosions and gunfire could be heard across the city on Monday night and clashes spilled over into Tuesday morning.
Another US army spokesman, Captain Brian O’Malley, said the clashes erupted when fighters attacked US forces carrying out routine patrols.
“We just kept coming under fire,” he said.
A spokesman for al-Sadr’s office in Sadr City said the clashes were a result of “arrest operations and provocative action carried out by the US forces every day”.
“We are ready to hold negotiations similar to those which have taken place in Najaf”
“US forces, tanks and helicopters raid the city every day using toxic gases. Houses and shops are being stormed every day,” Raed al-Kadhemi said.
“We are holding current negotiations with the Iraqi interim government to end this crisis,” he said, but “the daily raids are foiling our attempts”.
He added: “We are ready to hold negotiations similar to those which have taken place in Najaf.”
The renewed fighting came after a period of calm in the impoverished neighbourhood after the Shia leader called on his followers last week to observe a ceasefire.
But al-Sadr aides later said peace talks in Sadr City between his representatives and interim Prime Minister Iyad Allawi’s government had stalled, with the authorities rejecting the militia’s demands for American troops to keep out of the troubled district.