The attacks are among the most significant in Baghdad since insurgents led by the Islamic State extremist group captured Iraq's second-largest city Mosul last month at the start of its blitz across Iraq.
After Mosul's fall, the government moved aggressively to try to secure Baghdad amid fears it might fall as well, and the city has seen few major attacks in recent weeks.
Later in the day, three car bombs in different neighbourhoods of Baghdad went off in less than 10 minutes, hitting the districts of Baiyaa, Jihad and Khazimiyah. The attacks killed at least 15 people and wounded another 42, police officials said.
Another car bomb near a bus stop in Khazimiyah killed three people and wounded 15, police said. Hospital officials in Baghdad confirmed the casualty figures in all of the attacks.
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The Sunni militant blitz, led by the Islamic State extremist group, has pushed into areas west of Baghdad, and also has established a presence in a belt of Sunni areas running south and north of the capital. Baghdad itself has a predominantly Shiite population.
The Iraqi military launched a counteroffensive late last month to try to dislodge insurgents from the city of Tikrit, some 130 kilometres (80 miles) north of Baghdad. That effort has secured much of the highway between Tikrit and the city of Samarra, home to one of the most important Shiite shrines, but Tikrit itself remains in militant hands.