In the first attack, a parked car exploded near a police patrol in a main street in the center of the western city of Ramadi, police said. One policeman was killed in the morning blast in the city that was once an al-Qaeda hotbed.
An official in the nearby Ramadi hospital said five other policemen were seriously wounded. Two passers-by were also wounded, he said.
Several hours later in Baghdad, a suicide bomber detonated his explosive-rigged belt at a checkpoint after policemen suspected him of being an insurgent and opened fire.
Two Baghdad police officials said two policemen and a passer-by were killed and nine others including three policemen were wounded.
The casualties were confirmed by a medic at the capital's al-Yarouk hospital.
Earlier in Baghdad, double blasts took place in the southern district of Karradah. The first bomb, which was planted under a parked car, caused no casualties.
The second blast came a few minutes later as police and security forces rushed to the scene. It wounded six people including four security officers, police and health officials said.
All officials spoke on condition of anonymity because they were not authorized to release the information.