Iraq's premier fighting force has lost 40 per cent of its men in the battle to liberate Mosul from Islamic State control.



The Counter Terrorism Service, an elite US-trained unit, suffered the huge loss as it spearheaded the fight to drive militants out of Iraq's second city and IS's final stronghold in Iraq.



While the Baghdad government has refrained from divulging its battlefield losses, the figure was revealed in a US Department of Defense budget document, requesting $1.269 billion to rebuild, equip and train the unit to 20,000 personnel over the next three years.



"Requested funding will be essential in rebuilding CTS combat power that suffered 40 per cent battle losses in Mosul," it said.



It added: "These funds will be used to replace combat loss vehicles and equipment, while training and equipping the personnel to rebuild this force amidst continuing casualties."



Since October, the CTS, Iran-backed Shia militias, Kurdish peshmerga, Iraq security forces and a US-led international coalition, have fought to dislodge IS from Mosul in what has been described as the biggest urban battle since the Second World War.



Almost one million residents were displaced during the eight-month battle, with civilian casualties also high.



The Iraqi government has continuously refrained from publicising the casualty figures for government troops and paramilitary forces but the death toll is estimated to be heavy.



The UN came under criticism from the Iraqi military in December 2016 after reporting that nearly 2,000 members of the Iraqi forces had been killed in November alone.



Baghdad disputed the figues, saying the number was "not accurate and much exaggerated".

Meanwhile, airstrikes and exchanges of gunfire could still be heard in the narrow streets of Mosul's Old City on Monday, where IS has staged its last stand.

While patriotic celebrations took place in other parts of the city, Prime Minister Haider al-Abadi's spokesman, Saad al-Hadithi, said victory would not be formally declared until the few remaining militants were cleared from Mosul.