The U.S. military said that it responded to several attacks by militants with precision strikes, but only confirmed killing three militants. Two of the militants were killed in a Hellfire missile strike by an attack aircraft, according to the military. U.S. soldiers also suppressed "enemy fire" in four other clashes with tanks and attack aircraft, the military said.
The clashes erupted late Monday, just hours after Iraq's main Shiite political bloc and supporters of firebrand cleric Muqtada al-Sadr signed a cease-fire with the hope of ending seven-weeks of fighting that has left hundreds of people dead in the capital.
It was not immediately clear if the those killed in the clashes, which escalated early Tuesday, were militants or civilians. There were women and children among the wounded, said hospital officials, speaking on condition of anonymity because they were not authorized to talk to the media.
The military said Tuesday that militants staged several attacks on U.S. soldiers in Sadr City and elsewhere, but there were no troop casualties.
"They are obviously not listening to any agreement," Lt. Col. Steve Stover, a military spokesman for American troops in Baghdad, said. He accused what he called "special groups" of launching attacks on U.S. and Iraqi troops.
The U.S. military has alleged that most Shiite extremists fighting Iraqi and U.S. forces in Sadr City have splintered away from al-Sadr's Mahdi Army, and the cleric's level of influence over those rogue groups is unclear. Many are thought to be trained and armed by Iranian forces. Iran denies the allegations.
Stover also blamed the so-called "special groups" for a failed surface-to-air missile attack on a helicopter gunship over Sadr City on Saturday. The missile was fired from an unknown location in eastern Baghdad but missed the target, he said.
The missile harmlessly exploded, and the rocket body landed in the Azamiyah neighborhood, where it was recovered by allied Sunni fighters and handed over to the U.S. military.
The missile attack came a day before the four-day cease-fire went into effect Sunday. But there has been sporadic fighting since then.
The talks between al-Sadr's representatives and the United Iraqi Alliance over the details of the truce were not finished until Monday. The deal allows Iraqi forces to take over security in the militia stronghold of Sadr City, a Shiite slum that is home to about 2.5 million people, on Wednesday.
The clashes first erupted in late March when Iraqi forces launched a crackdown in the southern city of Basra and Shiite extremists began firing rockets and mortars from Sadr City toward the heavily fortified Green Zone, which houses the Iraqi government and Western embassies.
"Any attack against residential areas, government offices and the Green Zone are prohibited from Sadr City or from another area," the cease-fire agreement said.
Under the compromise deal, Iraqi forces will try to refrain from seeking American help to restore order. The U.S. military officials on Sunday said they were supporting the government forces and would take their lead.
The Sadrists rejected calls by Prime Minister Nouri al-Maliki to surrender weapons. But they gave the green light for Iraqi security sweeps, saying Mahdi fighters have no "medium or heavy weapons."
The majority of the 60,000 strong Mahdi Army has not openly participated in the fighting. Instead, they adhered to a general cease-fire ordered last August by al-Sadr, which has been one of the key factors causing a steep drop in violence in the country.
The latest cease-fire comes as the U.S. military largely finished the building of a barrier - reaching up to a height of 12 feet - to isolate extremists from using the southern section of Sadr City and disrupt supply and escape routes for militants.
In other developments: