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" declared by the jihadists 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.
Iraq's Joint Operations Command (JOC) 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 jihadists earlier in the offensive.
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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.
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.
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 today 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.
In Al-Danadan, streets were left strewn with rubble and windows blown out of many houses.
The recent fighting in west Mosul has forced more than 51,000 people to flee their homes, according to the International Organization for Migration.