"Anti-terrorism units affiliated with the Defense Ministry have successfully liberated the Old City's Al-Farouq neighborhood", Abdulamir Yarallah, commander of the army's ongoing campaign to recapture Mosul, said Monday.
He also estimated that there were only a few hundred Islamic State terrorists left in the city.
Another commander, Staff Lieutenant-General Abdulwahab al-Saadim, predicted, "We will finish the operation within a few days".
Iraqi forces battled deep into the devastated historical heart of Mosul and closed in fast on the last pockets of militants on Sunday, eight months into an epic battle to retake the city.
It was from a pulpit in that mosque that the extremists' leader, Abu Bakr al-Baghdadi, declared a caliphate in the lands they had seized in Iraq and Syria in July 2014.
But more than 100,000 civilians, half of them believed to be children, are still trapped, with little food, water, or medical treatment.
Iraqi troops captured on Monday the neighborhood of al-Faruq in the northwestern side of the Old City, facing the mosque, the military said. They said the militants ordered families to leave the area, likely in preparation for their final stand.
None were visible on Tuesday in government-controlled parts of the Old City.Only a handful of neighbourhoods remain outside the control of Iraqi forces, and while authorities expect the offensive to end in the coming days, their advance remains arduous.In the courtyard of a dilapidated home, a soldier launches a white commercial drone.
Iraqi special forces have opened up roads for civilians to escape in Mosul.
The CTS is leading the fight in the densely populated maze of narrow alleyways of the historic Old City which lies by the western bank of the Tigris river. Witnesses said they saw residents fleeing the area.
"Sleeper cells" left behind after the militants were driven back through Mosul's streets on Sunday attacked Iraqi forces and burned houses.
A USA -led Arab-Kurdish coalition is closing in on the extremists as well in Raqqa, their final major holdout in Syria.
It launched a wave of such attacks late on Sunday, trying to take control of a district west of the Old City, Hay al-Tanak, and the nearby Yarmuk quarter.
An Iraqi girl is seen as she celebrates Eid al-Fitr, in Mosul, Iraq on June 25, 2017.
Maj Gen Rupert Jones, the British deputy commander of the worldwide coalition fighting against Isil, said those left would be "cleared" by local forces. "The end is going to be very soon.it will take days", he said from the Old City.
A senior Russian diplomat on June 22 said al-Baghdadi was likely killed in a Russian air strike, although the claim has yet to be confirmed.