The United Nations has said it is expanding camps for displaced people around the battered Iraqi city of Mosul as the number of displaced people hits 300,000, and a US-backed assault on ISIL there continued.

The UN Office for the Coordination of Humanitarian Affairs said on Tuesday that a total of 392,000 people had fled their homes since the Iraqi government offensive to push the Islamic State of Iraq and the Levant group from the city began in October. Some 94,500 have since returned, it said.

The International Organization for Migration puts the number of displaced at 302,400.

Mosul had a pre-campaign population of about a million and half, split more or less evenly between the sides lying east and west of the Tigris river, which runs through its middle.

Iraqi forces captured the eastern side in January, and in February launched a second phase to take the western side, with air and ground support from a US-led coalition.

They are now battling to take the northwestern part, but the civilian death toll has mounted in the densely populated Old City, where the fighters are dug in.

More people are expected to flee the fighting and camps for the displaced north and east of Mosul are expanding, the UN statement said.

ISIL commanders killed

Bombing raids on the city by the Iraqi air force resumed on Tuesday as the sky cleared after several days of bad weather, the Iraqi military said.

A number of ISIL commanders were killed in an air raid on a position in Hay al-Tanak, a stronghold of the group in the west of Mosul, the army said in statement.

Among those killed were commanders in charge of booby traps, of suicide fighters and child recruitment, the statement added, without identifying them by name.

The improved weather should also allow ground forces to resume their advance towards the Grand al-Nuri Mosque, where ISIL's leader, Abu Bakr al-Baghdadi, declared a "caliphate" nearly three years ago over parts of Iraq and Syria.