At least 15 people were killed after a car bombing outside a restaurant in the town of al-Shumali, which is about 55 miles south of Baghdad.
Officials said local police were at the restaurant having breakfast. It's not clear how many officers are among the dead.
The blast also wounded 41 people. So far no one has claimed responsibility for that attack.
Earlier, gunmen opened fire on a security patrol in a mixed Sunni-Shiite neighborhood in northeastern Baghdad. The gunmen escaped after killing two policemen and wounding a third, officials said.
The other attack happened half an hour after the al-Shumali blast about 100 miles away. A bomb hidden on a bus carrying soldiers to a training area in western Iraq's Anbar province exploded. Two soldiers were killed and 11 were wounded.
The three deadly attacks revealed how vulnerable Iraqi forces remain to attacks after more than eight years of war.
The Associated Press contributed to this story.