"The counter-terrorism service and the rapid response forces have retaken the government compound in the center of Fallujah," the operation's overall commander, Lieutenant General Abdulwahab al-Saadi, told AFP.
Raed Shaker Jawdat, Iraq's federal police chief, confirmed the advance, which marks a significant step in the nearly four-week-old offensive to retake the city.
"The liberation of the government compound, which is the main landmark in the city, symbolizes the restoration of the state's authority" in Fallujah, he said.
Both commanders said their forces had met limited resistance from ISIS fighters during the push into the city center.
The government lost control of Fallujah in 2014, months before Daesh took second city Mosul and swept across large parts of the country.