But the militants are positioning themselves to defend the remains of its so-called "caliphate" in Syria and wage an insurgent campaign in Iraq.
The extremists are carrying out what looks like an organised, fighting withdrawal: a core of fighters is holding out in the city using hundreds of thousands of civilians as shields, tying down and bleeding the Iraqi military in urban combat.
Meanwhile, the Pentagon and Iraqi officials say the senior IS leadership has escaped to regroup in Syria and the deserts along the border to prepare for the future.
The civilian population is perhaps the main reason IS fighters have been able to hold out so long and turn Mosul into such a grueling battle.
It took months for Iraqi forces to drive them out of eastern Mosul while trying to avoid high casualties among residents amid house-to-house battles.
Now some 2,000 militants, by a coalition estimate, are holed up in western Mosul with 700,000 civilians. IS fighters are holding most of those civilians hostage as shields, while forcing some to flee as cover for their troops.
The largest city in IS territory, Mosul provided the group significant financing from taxing the population, factories to make weapons and space to gather freely.
But the Islamic State group's durable organization ensures it can fall back to the next fight.
Last weekend, Iraqi forces completely encircled western Mosul by capturing the last road into the enclave of about 40 square kilometers (15 square miles), comprising some of the city's most densely built districts.
In the month since the assault on the west began, troops have retaken the city's airport, a sprawling military complex, the main government compound and a ribbon of neighborhoods on the southwest side of Mosul.
The offensive is being waged from three directions with two divisions of special forces and a force of federal police advancing along the Tigris River, which divides the city into its western and eastern half.
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