So far, about 60% of western Mosul has been liberated, according to a map from Iraq's Joint Operations Command.
The fighting has driven people from the city. On Sunday, 10,607 people arrived at refugee camps where field staff cared for them, Jassem Mohammed al-Jaff, Iraqi minister of Migration and Displaced, said Sunday.
Amid the battle, Iraqi paramilitary forces said they discovered a mass grave northwest of Mosul containing what are believed to be the remains of about 500 civilian prisoners.
Mosul has been a vital stronghold for ISIS since it took control in June 2014. The largest city under ISIS control in Iraq and Syria, it was the place from which the group first declared the establishment of its so-called caliphate.
Caught in the middle of this battle are as many as 800,000 civilians, according to the United Nations
The Iraqi Air Force has dropped millions of leaflets on western Mosul,
where food and water are scarce and electricity sporadic, warning residents of the ongoing offensive and telling them to remain in their homes if they feel safe. The leaflets advised residents to hang white flags or sheets outside their homes to indicate civilians are inside.
Iraqi forces have continued their push into Mosul's old city, an area of narrow streets and alleys.
Observers believe Islamic State militants have dug in deep there, knocking holes between adjoining buildings to allow them maximum mobility with minimum exposure to Iraqi and US drones and aircraft. ISIS has also built a complex system of tunnels and bunkers, and no doubt will unleash even more suicide car bombs as Iraqi forces move in.
US officials believe that around half the 5,000 ISIS fighters in Mosul at the start of the offensive last October were killed or severely wounded.
But that still leaves 2,500 militants alive, and clearly many are ready to fight to the death.
Mass graves discovered
Also on Sunday, Iraqi paramilitary forces announced the discovery of a mass grave northwest of Mosul containing the remains of around 500 inmates from Baidush prison.
The Popular Mobilization Units -- made of predominantly Shiite militias -- said the remains are believed to be those of civilian prisoners executed by ISIS when it took control of Mosul and surrounding areas in June 2014.
However, a spokesman for Popular Mobilization Units was more circumspect.
"We don't have an exact number of how many victims and we don't know who these victims are. The Iraqi Ministry of Health is sending a forensic expert team to the site and will take few days before we start understanding and knowing more about the mass grave," Haitham Miyahi said.
Iraqi government officials confirmed the discovery and echoed his comments.
Col. Sa'ad Qassem, spokesperson for the 16th division of the Iraqi Army, said he would not have further information until a specialized team arrived at the site on Monday.
Dr. Zaid Abbas, director of forensic medicine of the Iraqi Ministry of Health, said the agency was sending experts to dig up the graves and take DNA.