Almost half a million people have fled the Iraqi city of Mosul since military operations to retake it from the so-called Islamic State commenced, a figure a senior UN official has described as "staggering" amid warnings that relief efforts are being stretched to their limits.

Lise Grande, the UN's humanitarian coordinator for Iraq, said in a statement issued on Monday that while the "worst case scenario" prior to the launch of operations was that up to one million civilians might flee Mosul, already more than 493,000 people have done so.

“The sheer volume of civilians still fleeing Mosul city is staggering...” she said. “Mosul has pushed us to our operational limits...We’re doing everything we can but this has been a long battle and the assault on the old city hasn’t started."

Ms Grande said the battle in the western part of the city - where UN estimates say as many as 500,000 remain in IS-controlled districts - was "much tougher" than that in the east. 

"There are more trauma injuries, homes are being destroyed, food stocks are dwindling quickly and families are at serious risk because there isn’t enough drinking water," she said.

“Civilians in Mosul face incredible, terrifying risks. They are being shot at, there are artillery barrages, families are running out of supplies, medicines are scarce and water is cut-off. Nothing is more important than protecting civilians—nothing."

The UN says that more than 1.9 million people have received life-saving assistance since the battle for the city began including people who have fled and families who have stayed.