Iraqi Prime Minister Iyad Allawi has vowed to defeat militiamen who refused to disarm, saying they were "making things more difficult in Iraq".
Sadr City is named after Moqtada Sadr's slain father
His pledge came after deadly clashes between US troops and Shia militants in a Baghdad suburb and an attack on an oil pipeline in southern Iraq.
US forces also said on Sunday they had killed two Iraqi gunmen in separate incidents in northern Iraq, near Mosul.
"The government will not permit private armed groups to operate," he said.
"We will confront this with force... It seems that there are some elements in the Mehdi Army that insist on making things more difficult in Iraq outside of Najaf."
Mr Allawi's promise follows the end of a three-week standoff between fighters loyal to the radical Iraqi cleric Moqtada Sadr and US-led forces in the city of Najaf.
On Saturday, Sadr loyalists had clashed with US forces in the Sadr City district of Baghdad, leaving at least seven people dead.
The US military said eight mortar bombs fired at one of their positions had damaged an electricity sub-station and cut power supplies.
A spokesman said militants later fired two mortar shells into a group of civilians.
The agreement brokered by Shia religious leader Grand Ayatollah Ali Sistani to end the Najaf crisis had made no mention of the Shia militants' stronghold in Sadr City, or other areas they hold elsewhere in Iraq.
State Minister Kassem Daoud has said many of Mr Sadr's followers have not handed over their weapons, as agreed under the ayatollah's plan.
Mr Allawi said the turning-in of weapons was of "basic importance" and the government would not back down on the issue.
Sunday's pipeline attack occurred in the south Rumaila oil field, near the city of Basra.
The damaged pipeline, which transports oil to export terminals in the Faw peninsula, is in the same area where an explosion on Thursday damaged eight pipelines.