Residents of Sadr City told the BBC there was fierce fighting overnight.
In Najaf, where Mr Sadr is locked in a stand-off with US and Iraqi troops, gunfire reverberated on Thursday.
The cleric has offered to end the uprising if there is a truce, but Iraq’s government says he has “only hours” to leave the Imam Ali shrine.
The US military says the operation in Sadr City, which began on Wednesday, is “ongoing”.
US soldiers were said to be using loudspeakers to urge militia fighters to hand over their weapons.
