Security forces killed an Islamic State commander and four fighters in the Hamrin Mountains area of northeast Iraq on Sunday, the military said.

The Canadian commander of NATO's training mission in Iraq says he has a challenging job on his hands, but one that could be vital to promoting long-lasting stability in the country.

Islamic State fighters say they will 'fight to the death' for Mosul, as Iraqi military commanders said they would take full control of the city from the insurgents at any moment.

The historic district is the last still under control of the militants in the city which used to be their capital in Iraq.

Thousands of civilians fled Mosul overnight as Iraqi forces advanced north of a sprawling military base near the city's airport on Friday.

Iraqi forces pushed into the first neighbourhood in western Mosul on Friday and took full control of the international airport.

Iraqi military vehicles, some adorned with flowers and carrying Iraqi flags, drove past the cheering crowd gathered at the university complex, while soldiers showed a "V" for victory sign.

U.S.-backed Iraqi government troops on Sunday fully liberated the sprawling complex of Mosul University, an Iraqi military spokesman said, a major step in the massive operation to retake the Islamic State group-held city of Mosul.

The militants were fighting back at the university, which they seized when they took over the city in 2014.

Stiff resistance by the militants, civilians trapped inside their houses and bad weather have slowed advances.