Lt Gen Stephen Townsend told the BBC Iraqis needed to unite to ensure IS was defeated across the rest of Iraq.
He also urged the government to reach out to the Sunni Arab minority.
"If we're to keep... ISIS 2.0 from emerging, the Iraqi government is going to have to do something pretty significantly different," he said.
"They're going to have to reach out and reconcile with the Sunni population, and make them feel like their government in Baghdad represents them."
IS (also known as ISIS) seized control of much of northern and western Iraq three years ago after exploiting widespread Sunni anger at the sectarian policies of the country's Shia Arab-led government.
Iraqi Prime Minister Haider al-Abadi, who has promised to bridge the gap between the two Muslim communities, formally declared victory over IS in Mosul on Monday.
Standing alongside troops at a base in the city, he announced "the end and the failure and the collapse of the terrorist state of falsehood and terrorism ".
The US-led Coalition that provided air and ground support to Iraqi security forces confirmed they had Mosul "firmly under their control" but noted that areas of the Old City still had to be cleared of bombs and possible IS fighters in hiding…