Police said that at least 24 people were killed and 35 wounded in a roadside bomb attack at the popular central Baghdad market of Shorja on Wednesday.
A bomb in the nearby Karrada district killed two people and wounded 21 around the same time. A bomb went off near a busy petrol station, drawing a police unit in response.
Five officers were then wounded in a second explosion, when a car bomb detonated.
The blast in the Shorja market came just two hours after an explosives-rigged bicycle exploded near an army recruiting centre in Hilla, killing at least 12 people and wounding 28.
Police said that a man posing as a potential army recruit planted the explosives-rigged bicycle early on Wednesday outside the recruiting centre in central Hilla, about 95km south of Baghdad.
Hilla was the site of one of the
worst attacks in Iraq in 2005
It went off at about 8am (0400 GMT), when a crowd had gathered. It followed several days of heavy violence outside the capital.
Hilla was the site of one of the worst bomb attacks in Iraq, when a car bomber killed himself and 125 national guard and police recruits who were lined up to take physical tests in February 2005.
In another incident in 2005, an explosion killed 60 civilians who were lining up to apply for police jobs in the Kurdish city of Irbil in northern Iraq.