Iraqi officials say 11 militiamen have been killed and at least 19 wounded in clashes overnight with the U.S. military in Baghdad's Sadr City.
The U.S. military has only confirmed Tuesday that troops killed three gunmen in separate incidents after being attacked multiple times.
The fighting continues despite a cease-fire signed Monday by Shi'ite cleric Moqtada al-Sadr, whose militia is active in Sadr City.
The U.S. military said Monday that its soldiers killed three gunmen who attacked patrols in Sadr City the previous night.
Elsewhere, authorities said police in the northern city of Mosul arrested dozens of suspects in a crackdown on insurgents. Prime Minister Nouri al-Maliki told lawmakers Monday the operation will cover the entire province of Ninawa.
The White House on Monday welcomed the cease-fire for Sadr City, which was announced by the Iraqi government on Saturday. Spokeswoman Dana Perino said the Bush administration is pleased, but she warned that the situation is "fluid," and added that officials want to see how it progresses.
The truce was negotiated by Iraq's main Shi'ite political bloc and representatives of Moqtada al-Sadr.
Fighting in Sadr City has killed hundreds of people since late March when Mr. Maliki ordered a crackdown on armed Shi'ite factions.
The U.S. military has said repeatedly that it is fighting rogue elements of Sadr's Mahdi Army militia. The bulk of Sadr's forces are believed to have been adhering to a general cease-fire ordered by the cleric last August.
Some information for this report was provided by AP and Reuters.