The battle to wrest full control of the Iraqi city of Mosul from Islamic State will be over in a few days, the Iraqi military said on Monday, as elite counterterrorism units fought militants among the narrow alleyways of the historic Old City.

An attempted fight-back by militants failed on Sunday night and Islamic State's grip on the city, once its de facto capital in Iraq, was weakened, a senior commander said.

"Only a small part (of the militants) remains in the city, specifically the Old City," Lt. Gen. Abdul Ghani al-Assadi, commander of the Counter-Terrorism Service (CTS) in Mosul, told Reuters.