"There is only about one percent of the city of Mosul left in in the hands of Daesh (IS group) militants, and the Iraqi security forces are continuing their advance from several directions into of the old city center", JOC Spokesman Brigadier General Yahya Rasoul said on Sunday.
The Iraqi military didn't confirm ISIS statements that the insurgents took control of Hay al-Tanak and began attacking the nearby Hay al-Yarmuk neighborhood.
TRT World's Soraya Lennie reports from Mosul's Old City.
Lieutenant General Abdulwahab al-Saadi of the Counter-Terrorism Service (CTS) also stated, "The operation is continuing to free the remaining parts of the Old City".
A Reuters correspondent saw a young girl with facial injuries walking dazed and shocked across the frontline out of heavily-populated district with a group of neighbors. "They regrouped and launched counterattacks", he told the AFP news agency.
USA -supported Iraqi government offensives have wrested back several important urban centres in the country's west and north from Islamic State group over the past 18 months.
Al-Khodari told The Associated Press that IS sleeper cells set fire to houses and cars on Sunday afternoon in the Tanak neighborhood on Mosul's far western edge. "Partnered with them, our mission is to defeat ISIS in Iraq and Syria".
The fall of Mosul would essentially end the Iraqi half of the IS "caliphate" as a quasi-state structure. ISIL is facing an offensive in Raqqa, its self-declared capital in Syria.
Abadi said on June 22 that "we will declare a complete control over Mosul in the coming days".
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IS "members don't turn themselves in", Lieutenant Colonel Mohammad al-Tamim said.
"From a military perspective, Daesh is finished", Lt-Gen Assadi said, using an Arabic term for ISIS.
USA. -trained urban warfare units were channeling their onslaught along two perpendicular streets that converge in the heart of the Old City, aiming to isolate the jihadist insurgents in four pockets.
"The responsibility of this devastation is laid firmly at the doorstep of ISIS, and we continue to support our Iraqi partners as they bring these terrorists to justice".
The Iraqi army and interior ministry units are also battling ISIL fighters in the Old City's maze of narrow alleyways.
The battle headed toward the heart of Mosul City is still ongoing, with Iraqi government troops intending to open routes for escape for the many civilians who are still trapped in the area.
Iraqi authorities say Islamic State is trying to prevent them from leaving - so that they can be used as human shields.
But hundreds of other civilians have been killed in the past month as they tried to flee the Old City.