The reported firefight took place just a few streets away from the scene of a bombing that killed nine people outside a police station earlier in the day, exactly six months after US and British troops invaded the capital.
Shells could be seen littering the ground outside the offices of firebrand Shia Muslim cleric Moqtada Sadr's Mehdi Army, whose heavily armed members patrolled the area.
Tension rose earlier on Thursday after US troops searched the compound used by the militia, according to Shaikh Kaiss al-Kazaly, who leads Sadr followers in the populous Baghdad neighbourhood named after the cleric's family.
Militia members said the exchange of fire which killed one of their men and wounded two others started after US armoured vehicles entered Sadr City on Thursday night.
A loudspeaker placed over the militia's offices urged the armed men, some of whom held rocket-propelled grenade (RPG) launchers, not to shoot down US helicopters circling overhead.
There was no immediate US confirmation of the firefight, which came a few hours after a car bomb attack on a nearby police station killed the bomber and eight others and wounded 38 more people.
Three policemen were believed to be among the dead which includes at least five civilians, according to police.
Police Major Majid Abd al-Hamid said a driver drove through the gates of the compound and was fired at by policemen before detonating a bomb.
The attack happened just as policemen were lining up in the courtyard of the facility for the morning roll call.
Iraqi Sergeant Saad Drawal al-Dharaji said a local Shia Muslim cleric had earlier threatened police.
At least 38 people were wounded in the car bomb attack
"Last Friday at the mosque he threatened us. He sent us letters and sent letters to other police stations. He told the police to hand over a policeman for punishment because he said he had worked with Saddam Hussein's regime," he said.
Scores of US soldiers surrounded the building in Humvee vehicles.
Al-Sadr city is a densely populated area. A mosque near the scene was blaring warnings to the thousands of residents who had gathered at the station to leave the area for fear of a second explosion.
Early last month, a car bomb ripped through a major complex for Iraq's US-backed police force in the capital, wounding 14 people.
In related news, a Spanish military attache and intelligence officer in Baghdad was shot dead outside his home on Thursday morning.
Jose Antonio Bernal Gomez was an air force sergeant attached to Spain's National Intelligence Centre, said the foreign ministry.
He was chased from his home by three assailants and gunned down, barefoot and in his undershorts.
Bernal Gomez is the second Spanish official to die violently in Iraq since US President George Bush declared an end to major combat on 1 May.
Spain, which staunchly supported Washington's invasion, has contributed troops to the US-led occupying forces.
Meanwhile, one US soldier was killed in a rocket-propelled grenade attack on a convoy near the town of Baquba, 65km northeast of the capital early on Thursday, said a military spokeswoman.
Spanish officials said they would
not close the embassy
A US military convoy also came under attack in the flashpoint town of Falluja, but there were no casualties, said a witness.
Two helicopters arrived at the scene where forces found a second explosive device and detonated it.
Occupation forces have faced daily resistance attacks since the invasion of Iraq in March this year.
In the town of Huwaijah, US forces withdrew because of intense resistance attacks, according to a local official.
Occupation soldiers have detained about 1000 residents in Huwaijah, 80km northeast of Baghdad, fuelling frustrations in the area.
And in the northern city of Kirkuk, an apparent sabotage
attack on the electricity network left several districts without power for more than 24 hours, according to an electricity department official.
Officials do not know who was behind the blasts.