News of the advances came on the third day of a renewed offensive against the ISIS group in west Mosul - the largest remaining urban stronghold in the "caliphate" declared by the terrorists in 2014.
Supported by the US-led coalition bombing ISIS in Iraq and Syria, Iraqi forces began their push against west Mosul on February 19. The advance slowed during several days of bad weather but was renewed on Sunday.
Recent advances have brought government troops and police closer to Mosul's densely populated Old City, where hundreds of thousands of civilians are believed to still be trapped under ISIS rule.
Iraq's Joint Operations Command said in a statement that federal police and the elite Rapid Response unit had been able to "liberate" the headquarters for the Nineveh provincial government.
They also seized control of the Al-Hurriyah bridgehead, it said, in a step towards potentially relinking west Mosul with the city's east, which government forces seized from the terrorists earlier in the offensive.
All the bridges crossing the Tigris in Mosul have been damaged or destroyed, and Iraqi forces would either have to repair them or install floating bridges to reconnect the two banks of the river, which divides the city.
Officers said Tuesday that security forces had also managed to recapture the Mosul museum, where the terrorists destroyed priceless artefacts, releasing a video of their rampage in February 2015.