Two gunmen on Monday stormed the governor's headquarters in Arbil, the capital of Iraqi Kurdistan, opening fire and wounding a policeman, deputy governor Taher Abdullah said.
Kurdish security forces known as Asayish set up a "security cordon and are searching the building" for the assailants, Abdullah said.
The attack took place in the early morning before employees had arrived for work, witnesses said, adding that the gunmen were probably holed up on the third floor of the building.
It was not immediately clear what sparked the attack in the usually secure Kurdish regional capital.
The Islamic State jihadist group claimed a deadly attack on the interior ministry in Arbil in 2015.
The previous year the group was blamed for a suicide bombing that killed at least four people outside the Arbil Provincial Council Building.
Iraq declared victory over IS in December but the jihadists still hold pockets of territory and continue to carry out deadly attacks.
Kurdish peshmerga fighters took part in the battle against IS after it launched a 2014 offensive in Iraq, seizing nearly a third of the country.