In Kirkuk, at least two car bombs blew out a building that housed the local headquarters of the Kurdistan Democratic Party, killing 19 people, and another blast nearby killed at least four more, The New York Times reported.
Officials said at least 200 people were wounded.
Police said the target may have been the local office of Masoud Barzani, president of Iraq's semi-autonomous northern Kurdish region.
"This is a political explosion. Iraq is witnessing a political crisis that is being reflected on the security of the country and it's all because of the prime minister," Muhammed Kamal, chief of the Kurdistan Democratic Party in Kirkuk, told the Times.
There was no immediate claim of responsibility, police said.
In Baghdad Wednesday, gunmen killed three police officers at a checkpoint, police said.
Two women were killed in an attack west of Baghdad, officials said.
Security officials told IraqiNews.com a roadside bomb was detonated in northern Baghdad, injuring two people and causing damage to nearby buildings.