Also on Monday, four US troops were killed in a car bombing south of Baghdad.
"Four Task Force Baghdad soldiers were killed when a suicide car bomber attacked their checkpoint along a road south of Baghdad," said a military statement, without providing further detail.
The deaths bring to at least 2053 the number of US military personnel who have died in Iraq since the March 2003 invasion, according to an AFP tally based on the Iraq Coalition Casualty Count, an independent group that follows US casualties in Iraq.
A police patrol was hit by a blast in al-Dura district. Besides killing six police officers, the blast killed three civilians and injured 10 people, a security source said.
In a separate incident in the same neighbourhood two policemen were killed and two others wounded by an explosion that hit their patrol.
Two soldiers were killed and 14 injured in the late morning when a bomber blew up the car he was in at a checkpoint west of the northern oil city of Kirkuk, police said.
At sunset a police officer was shot dead in Kirkuk, local officials said.
In Mosul, Iraq's main northern city, two policemen were shot dead in two separate incidents by armed men, local police said. In Balad, 75km (45 miles) north of Baghdad, two Iraqis working at a US military base were killed on the spot and a third kidnapped by armed men. Their driver, however, was set free, police said.
The other five were all killed in incidents north of Baghdad, police and security sources said.