Brett McGurk, the senior US official in the counter-IS coalition, issued the warning after Iraqi forces cut off the last road out of the city, trapping IS fighters inside.
The jihadists have held Mosul, Iraq's second city, since 2014.
But Iraqi forces have managed to retake large areas in a months-long offensive.
They now control all of Mosul's eastern side, and the latest US-backed push against IS - which began on 5 March - has forced the extremists from key locations in the west, including the main local government headquarters and the famed Mosul museum.
Heavy fighting continued over the weekend, with Mr McGurk telling reporters in Baghdad on Sunday "just last night, the 9th Iraqi army division... cut off the last road out of Mosul".
He added "Any of the fighters who are left in Mosul, they're going to die there, because they're trapped.
"So we are very committed to not just defeating them in Mosul, but making sure these guys cannot escape."
Staff Major General Maan al-Saadi, of Iraq's elite Counter-Terrorism Service, said government forces now controlled "more than a third" of western Mosul.
He said he believed the fight would be easier than in eastern Mosul, which took 100 days to reclaim after the offensive was launched in October, finally falling in January.
However, federal police and rapid response units say they have now entered the Bab al-Tob area of the Old City, where the fight is expected to be tough due to its narrow alleyways through which armoured vehicles cannot pass.
Meanwhile, Joint Operations Command spokesman Brig Gen Yahya Rasool said he believed IS was weakening.
But he added: "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, and the operation is taking place with precision to preserve the lives of the citizens."
It is thought there may be as many as 600,000 civilians still trapped in IS-controlled areas of  Mosul.
The statements came a day after Iraqi forces said that  a "large mass grave" had been found near the city.
It contained the remains of hundreds of "civilian prisoners who were executed by (IS) gangs after they controlled the prison during their occupation of Mosul".
Any so-called Islamic State (IS) fighters left in Mosul will die in the Iraqi city, a US envoy co-ordinating the offensive has said.