Abadi had previously pledged the northern city would be retaken by the end of this year. But the operation has been slowed by concern to avoid casualties among civilians, who have mostly stayed in their homes rather than fleeing as was initially expected.
Asked to respond to comments by the commander of a U.S.-led coalition supporting Iraqi forces that it would take as long as two years to eliminate Islamic State and its cells in Iraq and neighboring Syria, Abadi said:
"The Americans were very pessimistic. They used to talk about a really long period, but the remarkable successes achieved by our brave and heroic fighters reduced that. I foresee that in Iraq it will take three months."
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Overnight the coalition bombed the last remaining bridge connecting the eastern and western parts of Mosul "to reduce enemy freedom of movement", a spokesman said on Tuesday.
A statement published by Amaq, a news agency supporting Islamic State, said the bridge was now completely out of service, and an unconfirmed video circulated online showed a segment of the span had fallen into the river.
The United Nations has previously expressed concern that the destruction of Mosul's bridges could obstruct the evacuation of civilians. Up to 1.5 million are thought to remain inside.
More than two months into the Mosul operation, elite Iraqi soldiers have retaken a quarter of the city, but entered a planned "operational refit" this month.
A U.S. battlefield commander told Reuters on Monday that Iraqi forces would resume their offensive in the coming days, in a new phase of the operation that will see American troops deployed closer to the front line inside the city.
Mosul, the largest city seized by Islamic State anywhere across the once vast territory it controlled in Iraq and neighboring Syria, has been held by the group since its fighters drove the US-trained army out in June 2014.
