A bomb in a bag exploded on Monday in the main market of the predominantly Shia city of Hilla, south of Baghdad killing several people.
Around the same time a bomb strapped to a motorbike killed seven people in a mainly Shia village near Baquba. Another 25 people were wounded in the blast in Khairnabat, witnesses and interior ministry sources said.
There was confusion over the death toll in Hilla. Interior ministry sources in Baghdad, citing Hilla police, said 17 people had been killed and 25 wounded. But a spokesman for Hilla police said only eight people had died.
Hilla, capital of the Babil province, has been a repeated target of attacks by Sunni Arab insurgents.
In May, 12 people were killed and 32 wounded when a car bomb ripped through a used car market in the city.
The worst attack in Hilla was on February 28, 2005, when a suicide bomber killed 118 people and wounded 147 after targeting municipal offices.
The US military confirmed that two soldiers found dead south of Baghdad last week had been abducted and killed by guerrillas. It said the bodies, "severely traumatised", had been found with a makeshift bomb between one of the soldier's legs.