The attacks on Wednesday came two days after politicians failed to draft a new constitution because of differences on basic issues, raising concerns of fresh political turmoil.
Two car bombs exploded 10 minutes apart at the bus station in the central district of al-Nahda, and a third exploded near al-Kindi hospital in the same neighbourhood.
"The casualty figure could rise as there are charred bodies all over the place," an Interior Ministry official said.
The figures were based on reports from four hospitals to which casualties were taken, he added, including the al-Kindi
hospital near the scene of the coordinated attack.
A dozen vehicles, including three police cars, were destroyed in the attacks at the al-Nahda station, a transit point for travellers heading to the southern provinces of the country.
It was unclear whether the police or the station was targeted in the initial blasts.
The first two bombs, shortly before 8am (0400 GMT), sent a huge plume of black smoke into the clear sky over the city.
The blasts sent plumes of black
smoke into the sky over the city
One went off close to an entrance to the al-Nahda station.
The blast left a two-metre-wide crater on the road, while mangled remains of a police car could be seen lying on top of another vehicle.
At least three buses were gutted by fire. The vehicles would have been packed with passengers at the time of the explosion.
A second went off inside, a few minutes later.
Bloodiest in weeks
About a quarter of an hour after that, as police and paramedics were moving casualties to al-Kindi hospital nearby, the third bomb detonated, killing some of those who had come to help.
"We heard an explosion in the garage, we went there and ran towards the buses for Kut, Basra and Amara," a witness, Ahmed Jabur, told Reuters at the scene.
It was unclear whether the police
were targeted in the blasts
"A coach blew up. When we were leaving, another one blew up in the middle of police cars."
The third blast exploded in a green part of the neighbourhood where people usually seek trees' shade in the blazing heat of Baghdad's summer, especially during the rush-hour.
It was the bloodiest attack in the capital in weeks.
The last bombing on this scale was on 29 July in northern Iraq.
Four US soldiers killed
A US soldier was killed in a roadside bombing and another three died when their vehicle overturned during combat operations in Baghdad this week, the US military said on Wednesday.
The latest deaths bring the total US military deaths to 1850 since the March 2003 invasion, according to Pentagon figures as of August 16. This month has been one of the bloodiest for American forces in Iraq.
Three soldiers died on Monday when their vehicle overturned into a sinkhole in southern Baghdad during combat operations, while the fourth was killed when his patrol was hit by a roadside bomb in the southwest of the capital on Tuesday.
Both incidents are under investigation, the military said.