The officer was gunned down after his car was intercepted in the center of Karbala, 50 miles south of Baghdad, health official Salim al-Abadi said.
Gunmen also opened fire on a foot patrol in eastern Baghdad, killing a policeman, police said. Another policeman was killed in a drive-by shooting in the northern city of Kirkuk.
A funeral was held Sunday for a former senior Baath Party official and his 5-year-old granddaughter. Both were gunned down Saturday night while driving in the Baghdad neighborhood of Dora, police said.
A mortar round hit a home in another area in Dora, wounding three children.
In other violence Saturday, gunmen on a motorcycle shot to death two men who were security officers during Saddam Hussein's regime as they were walking in separate locations of Karbala, police said.