The explosions, which followed in quick succession, struck a predominantly Shi'ite area of eastern Baghdad.
At least one of the attacks was reported to have been carried out by a suicide car bomber.
The explosions struck in an area in east Baghdad where many shops and businesses are located.
Reports say the first bomber drove his vehicle into the area and detonated his explosives. Shortly afterward, as a crowd gathered to help victims or simply to see what happened, another bomb in a nearby parked car exploded.
One witness at scene, an Iraqi Shi'ite man who gave his name as Ali, held up a cross and questioned whom such attacks were targeting.
"This is a blast in New Baghdad, and people here are Sunnis, Shi'a, and Christians," he said. "I want the world to see this [cross]. This belongs to one of our Christian brothers. We are all living here in the new Baghdad. All the sects are united. I want to ask the world, is this jihad? Where is the jihad?"
At least two of those killed and four of the wounded were reportedly policemen.
Abductions By 'Uniformed' Men
In another area of eastern Baghdad, gunmen dressed in police uniforms abducted eight people from an electronics shop. Reports said the gunmen dragged employees out of the store and bundled them into waiting cars before speeding off.
The U.S. military, meanwhile, said ground troops supported by aircraft destroyed a suspected militant hideout in the province of Diyala, northeast of Baghdad, killing 14 militants.
(compiled from agency reports)
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