Security forces, backed by tribesmen, managed to defend the complex in Ramadi, which lies 100 kilometres (60 miles) west of the Iraqi capital and is one of the last major urban areas in Anbar under Baghdad's control.
The attack by IS fighters on Ramadi, as well as clashes in the northern province of Kirkuk, follow gains made elsewhere by government forces battling to recapture ground from the Sunni extremists.
Four members of the security forces were killed and 21 wounded, according to the officer and a doctor.
Daraji said that more than 10 air strikes were carried out against the jihadists in Al-Hoz, an area from which security forces had pulled back, allowing the jihadists to advance to within striking distance of the key government buildings.
He said reinforcements had been deployed in the city.
Parts of Ramadi and all of Fallujah, to its east, have been outside government control since the beginning of the year, but much more of Anbar province has since been seized by IS, which spearheaded a sweeping June offensive that overran swathes of Iraq.
Iraqi security forces wilted under an initial IS onslaught in June, but are now backed by US-led air strikes, international advisers, Shiite militiamen and Sunni tribes, and have begun to claw back some areas.
They retook Jurf al-Sakhr south of Baghdad and also made important gains in the Baiji, Jalawla and Saadiyah areas north of the capital.
But three key cities, Mosul, Tikrit and Fallujah are still in militant hands, as are a slew of villages and other areas.
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