The operation to retake west Mosul -- Daesh largest remaining urban stronghold -- was launched on Feb. 19, but the advance had slowed in the face of several days of bad weather until a renewed push began Sunday.
"The heroes of the federal police and Rapid Response liberate the government building for Nineveh province and control the second bridge (Al-Hurriyah Bridge)," the Joint Operations Command said in a statement reported by AFP.
Mosul, Iraq's second city, is the capital of Nineveh province.
The city is divided by the Tigris River, and while bridges crossing it have been either damaged or destroyed, they would provide a link between the government-held east and Daesh-held west if they can be repaired or otherwise bridged.
The fighting in west Mosul has forced more than 50,000 people to flee, the International Organization for Migration said.
Daesh overran large areas north and west of Baghdad in 2014, but Iraqi forces have since regained most of the ground they lost.