“There’s about 2,000 remaining,” the official told reporters on condition of anonymity during a trip to Iraq by the new Pentagon chief, Jim Mattis.

The estimate which the US-led coalition supporting Iraqi forces gave before the October 17 launch of a huge operation on Mosul was that the city was defended by 5,000 to 7,000 jihadists.

The coalition has not provided figures but it has said that the four-month-old campaign on Mosul had inflicted heavy casualties on IS.

Tens of thousands of Iraqi ground forces, receiving air support from the coalition as well as from its own aircraft, are involved in the operation, seen as the culmination of efforts to retake the land the government lost to the jihadist organisation in 2014.

Commanders and experts expect that the fighting in west Mosul could be the bloodiest yet.

The neighbourhoods that lie west of the Tigris River that divides the city are densely populated, have narrow streets that will be impassable for some military vehicles and are home to populations that could be more hostile that on the east bank.

Mattis, a retired Marine general who commanded troops during the 2003 invasion of Iraq, has been touring the region and arrived in Baghdad early Monday on a unannounced visit. DM