The compound reportedly houses the provincial council as well as Anbar's police headquarters.
A second bomb blast followed a few minutes later when a man detonated his explosive vest some 500 meters away.
Anbar Governor Qassim Mohammed put the casualties from the attacks at seven dead and 28 wounded.
But a police official at the sit of the explosions said the death toll had risen to 17.
Most of the killed are police officers and 47 people have been wounded, he said on condition of anonymity, adding the blasts were caused by two successive vehicle bombs.
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