Fighting was intense around the Ramadi government compound, which houses most of the city's government offices, according to an Anbar councilman.
Officials said three near-simultaneous suicide car bombings targeting the compound killed 10 policemen in the city on Friday.
The attack was part of a new push by the ISIS group to capture areas still controlled by the government in the region.
Ramadi was a key stronghold of the insurgency in the US-led war in Iraq.
ISIS militants raised their black flag over the local government compound in the Iraqi city of Ramadi on Friday and claimed victory through mosque loudspeakers after overrunning most of the western provincial capital.
The insurgents attacked Ramadi overnight using six suicide car bombs to reach the city center, where the Anbar governorate compound is located, police sources said.