The advances, which also included the recapture of three neighbourhoods, were announced on the third day of a renewed offensive against the Islamic State group in west Mosul -- the largest remaining urban stronghold in the "caliphate" IS declared in 2014.
Supported by the US-led coalition bombing IS 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.
The latest gains have brought government forces closer to Mosul's densely populated Old City, where hundreds of thousands of civilians are believed to still be trapped under jihadist rule.
Iraq's Joint Operations Command (JOC) said in a statement that federal police and the elite Rapid Response Division had been able to "liberate" the Nineveh provincial government headquarters.
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 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 instal floating bridges to reconnect the two banks of the river dividing the city.
Officers said Tuesday that security forces had also managed to recapture the Mosul museum, where the jihadists destroyed priceless artefacts, releasing a video of their rampage in February 2015.
WATCH: Iraqi forces close in on Mosul
Site of artefact destruction
The video showed militants at the museum knocking statues off their plinths and smashing them to pieces. In another scene, a jackhammer was used to deface a large Assyrian winged bull at an archaeological site in the city.
"Rapid Response entered the museum... there is nothing there," Lieutenant Colonel Abdulamir al-Mohammedawi said.
The jihadists' attacks on ancient heritage in Iraq and Syria have sparked widespread international outrage and fears for some of the world's most precious archaeological sites.
The museum was on a police list released Tuesday of sites recaptured from IS, which also included Mosul's central bank building, which the jihadists looted along with other banks in 2014, seizing tens of millions of dollars.
Watch Iraqi forces retake government buildings:
The JOC also announced Tuesday that Iraqi forces had regained complete control of the west Mosul neighbourhoods of Al-Dawasa, Al-Danadan and Tal al-Ruman, and were advancing against the jihadists in other areas.
In Al-Danadan, streets were left strewn with rubble and windows were blown out of many houses.
"There were mortar rounds falling on us, they fell on the roof and in the courtyard," said Manhal, a 28-year-old resident of the area.
The recent fighting in west Mosul has forced more than 51,000 people to flee their homes, according to the International Organization for Migration.
But the number who have fled is still just a fraction of the 750,000 people believed to have stayed on in west Mosul under IS rule.
Emerging from the chaos of the civil war in neighbouring Syria, IS seized control of large parts of Syria and Iraq in mid-2014, declaring its Islamic "caliphate" and committing widespread atrocities.
Watch Iraqi forces battle IS in heavy west Mosul fighting:
Anti-IS advances in Syria
The US-led coalition launched air strikes against the jihadists in both countries several months later, and has backed both Iraqi forces and fighters in Syria battling IS.
The jihadists have been pushed from most of the territory they once seized but remain in control of key bastions including west Mosul and the caliphate's de facto Syrian capital Raqa.
In Syria, they have faced offensives by three rival forces.
Turkish troops and their Syrian rebel allies have pushed south from the Turkish border and driven IS out of the northern town of Al-Bab.
Syrian government troops have driven east from second city Aleppo with Russian support and seized a swathe of countryside from the jihadists.
The Syrian Observatory for Human Rights, a Britain-based monitor of the conflict, said Tuesday that regime forces had recaptured a key water pumping station that supplies water to second city Aleppo.
Iraqis continue to flee fighting in west Mosul:
"Regime forces took over the area of Al-Khafsa and seized the water-pumping station after the withdrawal of the IS jihadists," it said.
A US-backed alliance of Kurdish and Arab fighters has been advancing on Raqa, and on Monday reached the Euphrates River cutting the main road to the partly IS-held city of Deir Ezzor downstream.
World powers have vowed increased cooperation in tackling the global threat from IS, which from its base in Syria and Iraq has organised or inspired a series of deadly attacks in foreign cities.
Turkish, Russian and US military chiefs held talks on Tuesday in the southern Turkish city of Antalya on issues including cooperation in Iraq and Syria.
