ISIS fighters are now trapped in Mosul as Iraqi forces cut off the last road out of the city, the U.S. envoy to Counter Terrorism Service (CTS) Brett McGurk said.
Iraqi security forces recaptured control of more than a third of west Mosul from the Islamic State group since launching an assault on the area last month, a commander said on Sunday.
After "fully liberating" the city's east from IS in January, US-backed Iraqi forces moved onto western Mosul, with a renewed push in March.
"Our forces are resolved to advance toward the center of western Mosul", al-Talibi said.
"The battle is not easy... we are fighting an irregular enemy who hides among the citizens and uses tactics of booby-trapping, explosions and suicide bombers", Brigadier General Yahya Rasool said.
In mid-February, Iraqi forces - backed by a USA -led air coalition - began fresh operations aimed at dislodging Daesh terrorists from western Mosul.
Mosul has been a vital stronghold for ISIS since it took control in June 2014.
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Federal police and Rapid Response units said they entered the Bab al-Tob area of the Old City, amd expected tough fighting due to the alleyways being too narrow for armored vehicles.
About 40,000 people have fled the fighting and hardship in the past 10 days, bringing the total number of people displaced from Mosul since campaign started to more than 215,000, according to United Nations estimates.
One resident of Wadi Hajar district said that that a store giving out food aid exploded killing and injuring many civilians, including "young children".
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.
The Hashd al-Shaabi, or Popular Mobilization Forces, a government-sponsored coalition of local militias, said human remains in prison uniforms were found at the site when it was recaptured by Iraqi fighters last week.
Mr McGurk said ISIS had lost "over 60 percent of the territory it once held" in Iraq and was "losing more every day".
Iraqi archaeologists think that tunnels dug by Islamic State militants under a destroyed shrine in Mosul have revealed the palace of an ancient Assyrian king who ruled some 2,700 years ago.