Fierce fighting has shaken Mosul in recent days as thousands of US-backed Iraqi soldiers and police battle to reclaim the country's second city.
A renewed push against the jihadists launched last Sunday has seen IS forced from several neighbourhoods and key sites, including the main local government headquarters and the famed Mosul museum.
By Sunday, Iraqi forces were tightening the noose.
"ISIS is trapped. Just last night, the 9th Iraqi army division... Cut off the last road out of Mosul," the US envoy to the anti-IS coalition, Brett McGurk, told journalists in Baghdad.
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Staff Major General Maan al-Saadi of the elite Counter-Terrorism Service told AFP that "more than a third" of west Mosul was now under the control of security forces.
CTS forces were battling IS inside the Mosul al-Jadida and Al-Aghawat areas on Sunday, he said.
Iraq's Joint Operations Command (JOC) said that forces from the Rapid Response Division, another special forces unit, and the federal police were also attacking the Bab al-Toub area on the edge of Mosul's Old City.
IS resistance "has begun to weaken in a big way", he added.
IS seized Mosul in mid-2014 and swept across areas north and west of Baghdad, taking control of swathes of territory and declaring a "caliphate" straddling the border with Syria.
Backed by a US-led air strikes and other support, Iraqi forces have since retaken much of the territory they lost.
After recapturing the east of the city, Iraqi forces last month set their sites on the west, where hundreds of thousands of civilians remain trapped.
Northwest of Mosul, Iraqi forces on Saturday announced they had uncovered a mass grave containing the remains of hundreds of people executed by IS inside the infamous Badush prison, taken this week.