Iraqi forces are fighting for control of government buildings in Mosul on the third day of a renewed offensive against ISIL fighters in west Mosul.

The troops are pushing towards Mosul's Old City centre as they try to clear ISIL, or the Islamic State of Iraq and the Levant group, from the city altogether.

West Mosul is the largest remaining urban stronghold in the "caliphate" declared by ISIL, also known as ISIS, in 2014.

Iraqi forces said on Tuesday they had seized the main government offices in Mosul and its famed museum as part of their advances, which included the recapture of three neighbourhoods.

Supported by the US-led coalition bombing ISIL 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 troops and police closer to Mosul's densely populated Old City, where hundreds of thousands of civilians are believed to still be trapped under ISIL rule.

The Iraqi government says 65,000 people have left Mosul in an attempt to escape the fighting, while the Switzerland-based International Organisation for Migration says the number is 51,000.

However, the number who have fled is still just a fraction of the 750,000 people believed to have stayed on in west Mosul under ISIL rule.

Al Jazeera's Stefanie Dekker, reporting from Erbil, in northern Iraq, said many had been caught up in the violence.

She said in a ward run by an international NGO called Emergency there were civilians, including children, from around Mosul with injuries caused by bullets, shelling and bomb explosions among other things.

"It's a very difficult situation for the people of Mosul," she said.

Government gains

Iraq's Joint Operations Command (JOC) said in a statement on Tuesday 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 Hurriya bridgehead, it said, in a step towards potentially relinking west Mosul with the city's east, which government forces seized from ISIL 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 on Tuesday that security forces had managed to recapture the Mosul museum, where the fighters destroyed priceless artefacts, releasing a video of their rampage in February 2015.

The museum was on a police list released on Tuesday of sites recaptured from ISIL, which also included Mosul's central bank building, which the fighter looted along with other banks in 2014, seizing tens of millions of dollars.

The JOC also announced on Tuesday that Iraqi forces had regained complete control of the west Mosul neighbourhoods of Al Dawasa, Al Danadan and Tal al-Ruman, bringing the total number of recaptured areas to 10.

ISIL has been pushed from most of the Iraqi territory they once seized, but remain in control of key bastions including west Mosul and the caliphate's de-facto Syrian capital Raqqa.