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.
But IS has seen a stark reversal of its fortunes since then.
IS "is trapped. Just last night, the 9th Iraqi army division, up near Badush, just northwest of Mosul, cut off the last road out of Mosul," Brett McGurk told journalists in Baghdad.
Iraqi soldiers and pro-government paramilitaries are fighting IS west of Mosul, while two special forces units and the federal police battle the jihadists inside it.
"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," McGurk said.
In practice, IS fighters may still be able to sneak in and out of the city in small numbers, but the lack of access to roads makes larger-scale movement and resupply more difficult, if not impossible.
IS has lost "over 60 percent of the territory it once held here in Iraq, and is losing more every day," and is losing fighters faster than it can replace them, McGurk said.
Nearly 90,000 trained personnel
"We now believe that we are killing so many of their fighters that they are not able to replace them. That was not the case even a year ago," said McGurk, putting the toll for IS leaders at 180 dead.
In addition to carrying out strikes targeting IS, the US-led coalition has trained nearly 90,000 members of the Iraqi security forces, the US envoy said.
Washington had spent billions of dollars training and equipping Iraqi forces prior to its military withdrawal in 2011, but that effort did not translate into long-term competence, with Baghdad's forces performing dismally in the early days of the 2014 IS offensive.
Iraqi forces have since made a major turnaround, dealing IS a string of defeats and launching a massive operation in October to recapture Mosul.
While the noose is tightening around the jihadists still in Mosul, the city's recapture would not spell the end of IS.
It also holds areas in western Iraq as well as across the border in Syria, including Raqa, the only city aside from Mosul in which IS still holds significant territory.
The US-backed Syrian Democratic Forces, an umbrella group for Kurdish and Arab fighters, are closing in on Raqa, with McGurk saying that they were some 10 kilometres (six miles) from the city.
"Raqa remains their administrative capital, it's where we think a lot of their leaders are located, it's where we think they are planning a lot of attacks around the world," he said.