Earlier in the day, three mortar rounds exploded near the Abu Hanifa mosque in Baghdad, wounding a guard.
The mosque is one of the most important religious sites for Sunni Muslims in Iraq.
Sadr appeals for calm
A defence ministry official said that Friday's clashes were so intense that precise information was difficult to obtain.
"We couldn't intervene, neither us or the police - it was too fierce, so the Americans had to come in," said the official.
Al-Sadr appealed for unity in a statement on Thursday, while Iraqi leaders appeared on television urging calm. But a source at police headquarters said 30 people were killed and 48 wounded in violence in Hurriya.
Militia members set fire to the Nida Allah mosque in this mixed Sunni-Shia neighbourhood, next to the Shia bastion of Kadhimiyah, and then prevented firemen from dousing the blaze.
The defence official added that members of the Mahdi Army attacked the mosque with hand-held and rocket-propelled grenades, before going on to attack the houses of Sunni residents.
Also on Friday, a US helicopter fired on a funeral party in Baghdad, one of dozens taking place after Thursday's devastating bombings in Sadr City, in response to ritual shooting, the Iraqi interior ministry said.
A ministry official said two people were wounded.
Sunni leader's account
Adnan al-Dulaimi , a leading Sunni politician, said that mosques in Baghdad's Sunni al-Ameriyah and Ghazaliya neighbourhoods were also targeted by "terrorist militias".
"A large number of innocent civilians also died as the militias attacked apartments in the Salikh neighbourhood," al-Dulaimi said in a statement.