The city's historic centre is home to the Al-Nuri mosque, where IS leader Abu Bakr al-Baghdadi in July 2014 proclaimed an IS "caliphate" in jihadist-controlled territory in Iraq and neighbouring Syria.
The forces have recaptured several neighbourhoods from IS since starting the push for west Mosul last month, but the battle for the Old City, with its warrens of alleyways, was always expected to be tough.
Located on the west bank of the River Tigris which divides the city, the densely populated old centre is difficult for armoured vehicles to navigate and any use of heavy weapons there risks putting civilian lives in danger.
"The offensive has resumed in the same area as yesterday... Which is made up of large buildings, markets and narrow streets where the enemy is hiding," Brigadier General Mahdi Abbas Abdullah said.
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Several buildings have been retaken from the jihadists on the edge of the Old City in the past few days, Iraqi authorities have said.
But the fighting for IS's last major urban stronghold in Iraq puts civilians who remain in the Old City in "terrible danger", an aid coordinator for the United Nations has warned.
"Families are at risk of being shot if they leave and they are at risk if they stay," she said.
"It's horrible. Hundreds of thousands of civilians are trapped and they are in terrible danger."
Iraqi authorities launched the offensive to retake the city on October 17 last year, with the support of the US-led coalition that has been carrying out strikes against IS in Iraq and Syria since 2014.
Iraqi forces launched the drive to retake west Mosul on February 19, after seizing the city's eastern side the previous month.
More than 180,000 people have fled west Mosul, the Iraqi government said today.
About 111,000 have sought shelter in 17 nearby camps and reception centres while many others have stayed with relatives, the ministry of displacement and migration said.