The assault came in Hawijah, a Sunni Arab town in ethnically mixed Kirkuk province near which security forces stormed an anti-government protest camp in April, triggering Iraq's deadliest day this year.
One suicide bomber detonated an explosives-rigged vehicle near a police station, while a second blew up another near a local administrative building.
Militants then hit both buildings and a local council office with mortar fire, and gunmen clashed with the army.
Troops were combing the area for another nine assailants who were believed to have escaped, Dulaimi added.
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The Hawijah assault came a day after militants attacked two police stations and a local official's house in two towns northwest of Baghdad, killing seven police and the official's brother.
In the capital, six members of a single family were shot dead today, officials said.
A man, his wife, their three children aged between three and six, and another woman were killed in the Shaab area of east Baghdad, officials said, while at least one person was killed and nine wounded by a bomb near a cafe in the capital.
And a bomb killed three people and wounded 25 in Mosul, while one person was also shot dead in the northern city.
Prime Minister Nuri al-Maliki said in speech today that there has been "killing by identity card and name", referring to the selection of victims on the basis of the confessional or ethnic affiliation given away by their family or given name.
There are persistent fears that Iraq will return to the all-out Sunni-Shiite sectarian violence that peaked in 2006-2007 and killed tens of thousands of people.