The blasts in the town of Jalawla, north of Baghdad, also wounded 40 people, police Captain Farhad Rifat said.
The car bomb went off close to an office of President Jalal Talabani's Patriotic Union of Kurdistan (PUK) party and a Kurdish asayesh security forces building, Rifat said.
As emergency workers came to the scene, the suicide bomber entered the PUK office and detonated explosives.
There was no immediate claim of responsibility for the attacks, though suicide bombings are a tactic mainly employed by Sunni Muslim militants in Iraq.
More than 900 people were killed last month, according to figures separately compiled by the United Nations and the government.
So far this year, more than 4,500 people have been killed, according to AFP figures.
Officials blame external factors for the rising bloodshed, particularly the civil war in neighbouring Syria.
But analysts say widespread Sunni Arab anger with the Shiite-led government has also been a major factor.
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