People living in the Sadr City area told the BBC that there were fierce gun battles overnight between the American forces and the Shia fighters.
There was also fighting in Najaf on Thursday, where Mr Sadr is occupying a shrine with his armed supporters.
Mr Sadr has offered to end his uprising if there is a truce.
If he doesn't give himself up, they say he will face military action.
The people who live in Sadr City are stuck in their homes as fighting continues.
Mr Sadr says he will only stop the fighting if the US army show they will not go after his Mehdi Army.
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