The Kurdish-led Syrian Democratic Forces launched an offensive to capture Raqqa from the extremists on June 6, under the cover of airstrikes by the USA -led coalition.
The Old City is a densely-populated warren of narrow alleys where fighting is often done from house to house, according to Reuters. It said leaflets were distributed urging civilians to leave through five "safe corridors".
It is reported that there are 100,000 civilians remain trapped in the city.
"The army, counterterrorism forces and federal police launched an attack on the Old City", Staff Lieutenant-General Abdulamir Yarallah, who commands operations in Iraq's Ninevah province, said in a statement on Sunday.
The Old City of Mosul is the only district still under control of the militants in the northern Iraqi city, which used to be the group's capital in Iraq. It lasted until January in the neighbourhoods east of the Tigris River, and a month later, troops began their assault on the western half of the city. "Air and artillery strikes will be limited because the area is heavily populated and the buildings fragile", CTS spokesman Sabah al-Numan told al-Hadath TV in Dubai.
As for Raqqa itself, the US -backed Syrian Democratic Forces (SDF) are on the offensive to strip IS of one of its key strongholds and self-declared capital in Syria.
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"We are trying to be very careful, using only light and medium weapons.to avoid casualties among civilians", CTS divisional commander Major General Maan Saadi told Iraqi state TV.
According to the Interior Ministry's statement, Iraqi police, army and anti-terrorism forces have jointly begun advancing towards the region from three sides.
Bruno Geddo, the United Nations refugee agency's representative in Iraq, said ISIL had been capturing civilians and forcing them into the Old City.
But she said extensive planning and coordination with Iraq's military had allowed the humanitarian community "to stay just one little tiny step ahead" while it rushed to build new camps and find spaces in existing camps for families returning to already liberated eastern Mosul.
- March 14: Iraqi forces say they have captured the city's train station after reaching other symbolic sites such as the regional government headquarters and the city's museum.
The US-backed military offensive to recapture the Iraqi city entered its ninth month on Friday.
ISIL has lost much of that territory over the last three years, and Mosul is their last urban bastion in Iraq.