The pre-dawn clashes, started at 3am (midnight GMT) and 6am on Friday in the poor neighbourhood of Sadr City and claimed the lives of nine militia men, an al-Mahdi Army member said
At the local hospital, three wounded civilians were brought in, said Dr Jabbar Sulak.
The US military said there were few incidents over night and nothing that qualified as major fighting.
US troops and al-Sadr's militia has battled in the district of 2.5 million people since August when fighting, which has since ended, erupted between the sides in the Shia shrine city of Najaf.
Al-Sadr loyalists blocked
Also on Friday, Iraqi police prevented supporters of Muqtada al-Sadr from holding their weekly prayers at Kufa mosque, an AFP correspondent said.
Policemen fired into the air to disperse the crowds gathered to pray at the town's grand mosque as they chanted pro-Sadr slogans.
The mosque has been closed since a US-led assault on nearby Najaf, 160km south of Baghdad, in August which ended with the exit of al-Sadr's militia from the Imam Ali mausoleum on the orders of Grand Ayat Allah Ali al-Sistani, the most prominent figure in Iraq's Shia religious authority.
Since then, US and Iraqi forces have been clamping down on al-Sadr's movement, raiding its offices in Najaf and arresting nearly 40 of his deputies and partisans and pounding his militia's positions in Baghdad's Sadr City district.