The operation to retake west Mosul -- IS's largest remaining urban stronghold -- was launched on February 19, but the advance had slowed in the face of several days of bad weather until a renewed push began on 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.
Mosul, Iraq's second city, is the capital of Nineveh province.
The fighting in west Mosul has forced more than 50,000 people to flee, the International Organization for Migration said.
IS overran large areas north and west of Baghdad in 2014, but Iraqi forces backed by US-led air strikes and other support have since regained most of the ground they lost.