Monday's battles came one day after the US military said 19 had been killed in the same area.
"Fourteen of the insurgents were members of rocket-propelled grenade launcher teams, one was part of a mortar team engaging a coalition base and the final one was killed when he fired on a coalition patrol," the US-led military said in a statement.
"No coalition force casualties or damage to vehicles or equipment were reported," the statement said.
Earlier, Brigadier General Mark Kimmitt told reporters US troops and fighters loyal to al-Sadr had fought running battles in the alleys of the impoverished neighbourhood before and after US forces destroyed Sadr's office in the area. He said 35 militiamen had been killed.
But Mahdi Army commanders say US spokesmen are exaggerating militia casualties.
The office was destroyed by a combination of gunfire from tanks, Bradley fighting vehicles and "perhaps helicopters", he said.
Local witnesses said earlier the office had been flattened by a bomb dropped from one of the US warplanes in the air at the time.