More than 80 people were injured in Monday's attacks, which happened in predominantly Shia areas in Diyala province.
The deadliest attack occurred in the town of Huwaydir, 4km north of Baquba. Police said a suicide car blast tore through a marketplace, killing dozens of people.
"A suicide bomber driving a booby-trapped vehicle blew himself up in the middle of the central market area in Huwaydir," a police lieutenant-colonel was quoted by AFP news agency as saying.
One Minute ISIL
Another suicide bomber drove his explosives-laden vehicle past a checkpoint before blowing himself up in Kanaan district, killing at least 10 people and wounding the same number, a police captain said.
ISIL, which controls large expanses of the country's north and west, said in a statement circulated online by supporters that the targets were "rejectionists", as the Sunni group refers to Shia Muslims.
The government in Baghdad pledged to apprehend the culprits and better secure the province, where a number of towns were captured by ISIL last year.
ISIL currently controls about a third of Iraq and Syria.
Cabinet proposal
Earlier, Iraq's cabinet approved a proposal by Haider al-Abbadi, the prime minister, to overhaul the government bureaucracy, scrapping three vice presidential posts and the offices of three deputy prime ministers.
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| More than 80 people were injured in Monday's attacks, which happened in predominantly Shia areas |
The six posts under threat represented various political and sectarian blocs in the government.
The plan also effectively would push out of government Minister Nouri al-Maliki, Abbadi's predecessor, widely criticised for inflaming sectarian tensions and appointing loyal, less-qualified senior officers to Iraq's military before ISIL's advance last year.
