The deadliest attack took place in Baghdad's Allawi neighborhood, a predominantly Shiite district near the Green Zone that is home to many government offices and foreign embassies. A police official said four civilians were killed and 12 wounded in that blast.
He said the casualties could have been much worse, but the area was not crowded early Monday because of a state holiday to commemorate the 1958 Revolution that overthrew the monarchy.
A second vehicle packed with explosives blew up near a string of car dealerships in Baghdad's southeastern Bayaa area, killing at least three people and wounding eight, the official said. The explosion also damaged several cars.
Baghdad has seen several small scale bombings, but no major attacks, since Sunni militants launched an offensive last month that has overrun much of northern and western Iraq. The blitz has caused jitters in Baghdad, where Shiite militias have joined security forces in recent weeks to try to boost security in the capital.
The Sunni militant push, which is led by the Islamic State extremist group, has slowed since its initial rapid gains, but on Sunday the insurgents swept into the town of Duluiyah, some 80 kilometers (45 miles) north of Baghdad. They seized the mayor's office, police station, local council and courthouse. They also blew up a bridge that links the town with the predominantly Shiite city of Balad nearby.
The Iraqi military launched a counterattack that drove the militants from part of the town. But on Monday the militants were still inside key government offices and sporadic clashes took place, a police and an army officers said.
All officials spoke on condition of anonymity because they were not authorized to brief the media.