In the capital, shortly before sunset, a bomb exploded near a soccer field in the southeastern Shiite-majority suburb of Nahrwan, killing three people and wounding 14 others, police said.
And in the northern city of Mosul, according to police, one person was killed when a sticky bomb attached to his car exploded.
Medical officials in nearby hospitals confirmed the figures. All officials provided details of the violence on condition of anonymity as they were not authorized to release information.
Also, authorities unexpectedly shut Mosul's airport, but they gave differing accounts of why.
The head of the Iraqi Civil Aviation Authority, Nassir Bandar, said the shutdown was done for maintenance reasons. A senior intelligence official cited unspecified technical matters, while an airport official and said the move was for security reasons.
The latter two officials spoke anonymously as they were not authorized to discuss the matter publicly.
Mosul, also a former insurgent stronghold, is about 360 kilometers (220 miles) northwest of Baghdad.
No one claimed immediate responsibility for the attacks. But coordinated car bombings and attacks on civilians and security forces are a favorite tactic of the Iraqi branch of al-Qaida. It typically does not lay claim to attacks for several days, if at all.
The attacks come as security forces stage sweeps aimed at arresting Sunni insurgent suspects in areas around the capital. It also comes a day after a high-level government-sponsored meeting between Sunni and Shiite politicians and officials to discuss ways to defuse sectarian tensions in the country.
But neither the security nor the political efforts appear to have dented the insurgents' ability to stage attacks at a high pace.
More than 4,000 people have been killed over the past five months alone. That includes 804 Iraqis killed just last month, according to United Nations figures released earlier this week. Market places, restaurants, coffee shops and funerals are favorite targets of militant groups seeking to sow havoc.
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Associated Press writers Sameer N. Yacoub, Adam Schreck and Qassim Abdul-Zahra contributed.