The first attack in Mosul occurred when a suicide car bomber attacked a U.S. patrol, the U.S. military said. There were no American casualties, but five Iraqis were killed, including three young boys, the U.S. said.
Another suicide car bomber targeted Iraqi police in Mosul, 225 miles northwest of Baghdad. Twenty-five people were wounded, the U.S. said.
In Baghdad, a parked car bomb exploded in a commercial street in the Bayaa district, killing seven people and wounding nine others, police said. They spoke on condition of anonymity because they were not authorized to release the information.
The southwestern Baghdad neighborhood was the scene of bitter Sunni-Shiite fighting until last year when the U.S. troop "surge," the Sunni revolt against al-Qaida and a cease-fire by anti-American cleric Muqtada al-Sadr brought down violence to its lowest level in four years.
"Several car bombings have occurred on this street but no measures were taken to prevent these events," one Bayaa resident, who gave only his nickname Abu Ibrahim, told Associated Press Television News. "Where is the government? Where are the security officials to prevent such attacks?"
Attacks have been continuing in Mosul, Iraq's third largest city, despite months of U.S. and Iraqi security operations against al-Qaida and other Sunni extremist groups.
The governor of the province that includes Mosul, Duraid Mohammed Kashmoula, said Saturday that about 3,000 Christians have fled the city over the past week alone to escape threats and attacks by Sunni extremists.
He called on the government to step up military operations against Sunni extremists in the city.
U.S. officials are concerned that violence may rise in the run-up to provincial elections, which are expected by the end of January. Voters will select ruling councils in most of the country's 18 provinces. No date for the election has been set.
On Sunday, the spokesman for the election commission, Qassim al-Aboudi, told reporters that a total of 440 provincial seats would be contested, with 57 of them in Baghdad.
About 20,000 people have been trained as election monitors, he said.