In Baghdad, the first car bomb exploded around mid-morning at the entrance to the Kazimyah market, two police officers said. When panicked shoppers tried to flee the area, a second parked car exploded a few meters (yards) away, according to the officers.
The twin blasts turned several nearby cars into tangled piles of metal.
At least 17 people were killed and 45 were wounded in the two blasts, police said. All the victims were civilians.
About an hour later, two car bombs exploded simultaneously at the Shomali market, killing at least 14 people and wounding 36, two police officers said.
The car bomb on the edge of Karbala killed five and wounded 16, police said.
Health officials confirmed the casualty figures in each attack. All officials spoke on condition of anonymity as they were not authorized to release information.
Violence has dropped in Iraq since the worst sectarian fighting in 2006-2007, but insurgents carry out near-daily attacks on security forces and civilians in an attempt to undermine the Shiite-led government.
The current spike comes just over two months ahead of the provincial election.
Hadi Jalo, an analyst at the Baghdad-based Political Decision Center for Strategic Studies, said he believes al-Qaida-linked militants in Iraq are trying to exploit the growing Sunni discontent.
"I believe that with this fertile atmosphere there will be more attacks ahead of the provincial elections," he said.