While the fight to retake the Iraqi city of Mosul from Islamic State group is going to be difficult, it is "possible" it could be complete before President-elect Donald Trump takes office, U.S. Defense Secretary Ash Carter said on Monday.

Some 100,000 Iraqi government troops, Kurdish security forces and mainly Shia militiamen are participating in the assault on Mosul that began on Oct. 17, with air and ground support from a U.S.-led coalition.

The capture of Mosul, the largest city under control of IS group, is seen as crucial toward dismantling the caliphate which the militants declared over parts of the Iraq and Syria in 2014.

"That is certainly possible and again it is going to be a tough fight," Carter said when asked if the recapture would be complete before Jan. 20, when Trump starts his presidency.

Islamic State militants retreating in the face of a seven-week military assault on their Mosul stronghold have hit back in the past few days, exploiting cloudy skies which hampered U.S-led air support and highlighting the fragile army gains.

In a series of counter-attacks since Friday, the IS fighters struck elite Iraqi troops spearheading the offensive in eastern Mosul, and attacked security forces to the south and west of the city.

"Obviously there (are) always weather issues ... the Iraqi security forces are prepared for any eventuality there," Carter said.

Iraqi officials say they continue to gain ground against the militants who still hold about three-quarters of the country's largest northern city.

But the fierce resistance means the military's campaign is likely to stretch well into next year as it seeks to recapture a city where the militants are dug in among civilians and using a network of tunnels to launch waves of attacks.

Carter did not say how the recapture could be completed before Jan. 20 in the face of resistance from Islamic State group.

In a separate speech in California on Saturday, Carter left the door open for U.S. and coalition forces to stay in Iraq after Islamic State militants had been removed.

"In Iraq in particular, it will be necessary for the coalition to provide sustained assistance and carry on our work to train, equip, and support local police, border guards, and other forces to hold areas cleared from ISIL group," said Carter, using an acronym for IS group.