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.
