Iraqi forces launched the operation Sunday to retake the district, the last part of Iraq's second city still held by Daesh after a months-long offensive, AFP reported.
Commanders say the terrorists are putting up fierce resistance and there are fears for more than 100,000 civilians believed to be trapped in the maze of narrow streets.
Staff Major General Maan al-Saadi, a top commander in Iraq’s elite Counter-Terrorism Service, told AFP that heavy fighting had resumed at dawn on Monday.
"At 6:00 a.m. we pushed deeper into the Old City and took control of new areas in the Faruq neighborhood," he said.
"Daesh resistance has been fierce," he added.
"They have blocked every entrance, planted IEDs (improvised explosive devices) and booby trapped houses our forces might be near," he said. "Penetrating was very difficult. Today the fighting is face to face."
The push into Mosul's historic heart on the west bank of the Tigris River marks the culmination of a months-long campaign by Iraqi forces to retake the terrorist group's last major urban stronghold in the country.
The US-led coalition battling Daesh in Iraq and neighboring Syria has backed the offensive with months of airstrikes.
The loss of Mosul would mark the effective end of the Iraqi portion of the cross-border "caliphate" which Daesh declared in the summer 2014 after seizing swathes of Iraq and Syria.
Iraqi forces stationed Humvees by the Grand Mosque on the retaken east side of Mosul, facing the Old City and mounted with speakers.
The loudspeakers blared messages to terrorists, telling them: “You have only this choice: surrender or die”.
Messages were also broadcast to civilians in the Old City, saying Iraqi forces “are about to end your suffering”.
Late on Sunday Iraqi forces dropped nearly 500,000 leaflets over the city, warning that they “have started attacking from all directions”.
The leaflets urge civilians to “stay away from open places and... exploit any opportunity that arises during the fighting” to escape.
The United Nations has said Daesh may be holding more than 100,000 civilians as human shields in the Old City.
Commanders have said the fighting is expected to be very difficult and could last weeks.
Surrounded by Iraqi forces on three sides and blocked on the other by the Tigris River that runs through Mosul, the terrorists are cornered.
Iraqi forces launched a vast operation to retake Mosul in October, seizing the city’s eastern side in January and starting an assault on its western part in February.