U.S.-backed Iraqi forces pressed an advance on neighborhoods under Islamic State control in Mosul on Monday as they seek to dislodge fighters entrenched in a central mosque before the holy month of Ramadan.

Seven months into the campaign to recapture Mosul, militants are besieged in its northwestern corner, home to the historic Old City center and the medieval Grand al-Nuri Mosque, where their black flag has been flying since June 2014.

"If we advance this quickly we can finish it in days," First Lieutenant Nawfal al-Dhari told Reuters at a house turned into a temporary base in the western Islah al-Ziraie district, retaken by Iraqi forces three days ago.

"These are the dying breaths. They are completely surrounded." He said the momentum was with Iraq's elite Counter Terrorism Service (CTS) despite continued resistance from Islamic State fighters in the group's last bastion in Iraq.

"If you trap a cat in a room, it will scratch," he said.

Military commanders and intelligence officials say they aim to take control of the mosque before Ramadan starts at the end of this month even if there are still pockets under militant control.