Up to 20,000 civilians are trapped in the last Islamic State group-held areas in Mosul's Old City, which Iraqi forces are battling to retake, a senior UN official said on Thursday.

More than eight months since the start of the operation to retake Mosul, IS has gone from fully controlling the city to holding a small pocket of territory on the west bank of the Tigris River.

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But the fighting against the last IS holdouts is heavy, and civilians caught in the middle of the battle are in “extreme danger,” UN humanitarian coordinator in Iraq Lise Grande told AFP.

“Our estimate at this stage is that in the final pockets of the Old City, there could be as many as 15,000 civilians, possibly even as high as 20,000.

“The people that are still trapped inside of these pockets are in terrible condition,” facing shortages of food, she said.

“They're in extreme danger from bombardment, from artillery crossfire. The (IS) fighters that are still there are still directly targeting civilians if they try and leave.”

The battle has pushed 915,000 to flee their homes, nearly 700,000 of whom are still displaced.

“We exceeded our worst case scenario more than a month ago. In our very worst-case scenario, we thought that 750,000 people would flee,” Grande said.

The damage caused by the fighting in west Mosul — and the cost of addressing it — is huge.

There are “44 residential neighbourhoods in western Mosul. Six are nearly completely destroyed… Twenty-two neighbourhoods are moderately damaged and 16 are lightly damaged,” Grande said.

Based on a preliminary assessment, the first phase of “stabilisation” in west Mosul — which includes basic services, infrastructure, housing, education and police stations — will cost $707 million.

That is nearly double the expected figure, “because the level of damage in western Mosul is far higher than what we feared it would be,” she said.

IS overran large areas north and west of Baghdad in 2014, but Iraqi forces backed by US-led air strikes and other support have since regained much of the ground they lost.

The recapture of Mosul will not however mark the end of the war against IS.

The jihadist group holds territory elsewhere in Iraq as well as in neighbouring Syria, and has been able to carry out attacks in government-held areas.