BAGHDAD, Iraq (CNN) -- Battles between U.S.-backed Iraqi forces and militants raged overnight and into Thursday in two Baghdad neighborhoods, leaving at least 11 dead, an Interior Ministry official said.
At least three people were killed in radical Shiite cleric Muqtada al-Sadr's Baghdad stronghold of Sadr City, and 21 were wounded, the official said.
Fighting in the northeast suburb of Husseiniya left at least eight people dead -- including women and children -- and three wounded, he said.
Fighting began in Husseiniya on Tuesday, and since then at least 24 have been killed in battles between coalition forces and al-Sadr's Mehdi Army fighters, according to the U.S. military and Iraqi officials.
In other violence on Thursday in Baghdad, a parked car bomb killed a civilian and injured five near one of the entrances to the International Zone, an Interior Ministry official said. The area, also called the Green Zone, is the heavily fortified district that houses U.S. and Iraqi governmental offices.
Three civilians died and 15 were wounded when a roadside bomb exploded in western Baghdad's predominantly Sunni neighborhood of Mansour, an Interior Ministry official said.
The fighting in Sadr City has been going on for several weeks. The U.S. military said it was reduced somewhat after al-Sadr called on his supporters to halt attacks on March 30, but remained high.
Then, on Saturday, al-Sadr issued what he called a "last warning" to the government and told his followers in Sadr City to fight the occupier.
Al-Sadr's supporters have accused Prime Minister Nuri al-Maliki's government of not holding up its end of the cease-fire agreement, which includes freeing non-convicted prisoners from the Sadrist movement and halting what they call illegal raids on the cleric's followers.
Elsewhere in Iraq, in a northern suburb of Baghdad called Rashidiya, U.S. and Iraqi troops Thursday killed four Iranian-backed Shiite militia members and detained five, the U.S. military said.
The coalition forces came under fire while trying to arrest a suspect they allege was receiving money and weapons from Iran, according to the military.
The military identified the four as members of "special groups" -- bands of Shiite militia members who had not heeded the cease-fire issued by al-Sadr.
In other developments in Iraq:
• U.S. and Iraqi forces Thursday captured a suspected al Qaeda in Iraq leader in the northern city of Mosul, according to the U.S. military. He is believed to have been involved in kidnappings and suicide bombings.
• Coalition forces Thursday killed a suspected member of al Qaeda in Iraq when he pulled a pistol after troops stopped his car in Baghdad.
• Coalition forces Wednesday killed three al Qaeda in Iraq militants and detained 11 suspects during operations targeting terrorist networks in central and northern Iraq, the U.S. military said.
• Two U.S. soldiers were killed Wednesday in Iraq when their vehicle rolled onto its side as it headed to a combat outpost in Salaheddin province, north of Baghdad, the U.S. military said.
Their deaths bring to 37 the number of U.S. troops who have died in Iraq in April, and to 4,049 the number of U.S. service members who have died since the war began. E-mail to a friend