"I could order the Mahdi Army to root out the terrorists and fundamentalists but this would lead us into civil war and we don't want that," the Shia cleric told a news conference in the city of Najaf on Monday.
Returning to a theme that has previously been common ground with Sunni fighters and appeared to give his followers some protection from them, al-Sadr renewed his criticism of the US forces, against which al-Mahdi Army rose up twice in 2004.
"I hold the occupiers responsible for this tragedy," al-Sadr said. "I consider them the ones who ordered it."
At least 46 people were killed and 204 were wounded in a crowded Sadr City neighbourhood east of Baghdad on Sunday, when up to six car bombs exploded in quick succession.
The attack raised new fears of Shia reprisals and all-out sectarian warfare, two-and-a-half weeks after the bombing of an important Shia shrine prompted days of violence, including assaults on Sunni mosques and homes that killed hundreds.