He said the exodus of civilians from the city's western side was still continuing.
They recaptured east Mosul earlier this year, and are now battling to retake its western side from the jihadist group, which seized the country's second city along with swathes of other territory in 2014.
Iraq's joint operations command said another special forces unit and federal police were attacking the Bab al-Toub area on the edge of Mosul's Old City.
USA -backed Iraqi forces pushed deeper into Mosul to take positions still held by IS militants.
"We are fighting an irregular enemy who hides among the citizens and uses tactics of booby-trapping, explosions, and suicide bombers, and the operation is taking place with precision to preserve the lives of the citizens", said Brigadier-General Yahya Rasool.
"Any of the fighters left in Mosul, they're going to die there".
CTS forces were battling IS inside the Mosul al-Jadida and Al-Aghawat areas in west Mosul on Sunday, said Saadi, adding that he expected the fighting there to be completed in the coming hours.
Coalition air support has been pivotal to Iraq's fight against ISIS, helping Iraqi forces slowly claw back territory throughout Iraq's western Anbar province and up the Tigris River valley to Mosul.
"As you can see the digging was very extensive and it includes a ramified tunnel network, with one tunnel leading to another in an attempt to dig as large an area as possible in order to unearth and loot artefacts", said Musab Mohammed Jassim of the Nineveh Antiquities and Heritage Department, describing what ISIL did as "an act of sabotage".
Losing Mosul would be a major blow to Islamic State.
As an array of forces dismantle Islamic State's self-proclaimed caliphate across Iraq and Syria, more evidence is emerging of the war crimes committed by the Sunni Islamist militants, who targeted Shi'ite Muslims and religious minorities as well as opponents from their own sect.
On Saturday, the Hashed al-Shaabi - an umbrella organisation for paramilitary groups that is dominated by Iran-backed Shiite militias - announced the discovery of a large mass grave northwest of Mosul.
A mass grave containing the remains of about 500 was found at Badush prison near Mosul, BBC reported.