At least three people were killed and 12 wounded during heavy fighting which lasted more than an hour in the Sadr City neighbourhood.
The US military said its soldiers came under fire when they arrived to arrest members of a suspected punishment and torture cell. One US soldier was injured, the statement said.
Iraqi government television and aides to Shia cleric Muqtada al-Sadr said US aircraft were called in to hit buildings in the area after the shooting started.
Jaleel al-Nouri, an aide to al-Sadr said: “Several aerial and ground raids began in central Sadr City. We can see several houses on fire.”
Mobile phone calls
Police said the fighting stopped when al-Mahdi Army members – who are loyal to al-Sadr – received calls on their mobile phone asking them not to confront US troops. It was not clear who made the calls.
Abdulzahra al-Suwaidi, another aide, claimed the raid had targeted the al-Mahdi Army to punish it for holding an anti-American and anti-Israeli street rally on Friday.
Al-Suwaidi said: “Because of the demonstration the occupation forces raided and carried out air strikes killing and wounding people and burning several houses.”
The al-Mahdi Army militia has been accused of taking part in sectarian and political murders across Baghdad in recent months.
US troops on streets
The US has increased its presence on the streets of Baghdad in an attempt to reduce the level of sectarian violence. About 3,700 soldiers of the 172nd Stryker Brigade Combat Team are taking positions in some of the most violent districts of the capital.
On Sunday, a roadside bomb killed three US soldiers southwest of Baghdad, the US military said.
Elsewhere, gunmen have shot dead at least six Iraqi soldiers and wounded 15 in an attack at a checkpoint near the northern Iraqi town of Baquba on Monday, police said.
Police Lieutenant Colonel Amer Naseer said the attack took place at dawn near the small town of Balad Ruz, 50km southeast of Baquba. One gunman was killed, he said.
The latest fatalities took the US military death toll in Iraq since the March 2003 invasion to 2,590.