Iraqi forces backed by US-led air strikes and other support are now battling IS inside second city Mosul, after retaking much of the other territory the jihadists had seized.
"Daesh controlled 40 percent of Iraqi land" in 2014, Brigadier General Yahya Rasool told reporters, using an Arabic acronym for IS.
"As of March 31 (this year), they only held 6.8 percent of Iraqi territory," said Rasool, the spokesman of the Joint Operations Command coordinating the anti-jihadist effort.
Various members of the forces, Iraqi and foreign, battling the jihadists have disagreed in the past on figures about control of territory, but IS has been losing ground steadily for close to two years.
The most brutal organisation in modern jihad shocked the world when it took over Mosul in June 2014 and then swept across much of the country's Sunni Arab heartland.
Its reach in Iraq peaked in August the same year when a second offensive saw it take over areas of northern Iraq that were home to various minorities and had been under the control of forces from the country's autonomous Kurdish region's forces.
Iraqi forces with the backing of the US-led coalition -- which has thousands of military personnel deployed in Iraq and carries out daily air strikes -- launched a major offensive to retake Mosul in October 2016.
- Coalition to stay -
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They retook control of the eastern side of the city, which is divided by the Tigris River, in January and have since mid-February been battling die-hard jihadists holed up in their last west Mosul redoubts.
The full recapture of Mosul, the de facto capital of the "caliphate" that IS proclaimed nearly three years ago, would end the jihadists' dreams of a cross-border state.
Speaking at the same press conference in Baghdad on Tuesday, the spokesman for the US-led coalition vowed that Iraq would not be abandoned after the recapture of Mosul.
"Once that task is accomplished, the coalition will be here to support our Iraqi partners as they eliminate IS from every corner of Iraq," Colonel John Dorrian said.
"Though the fighting is going to be very hard... this enemy is completely surrounded. They aren't going anywhere -- they will be defeated and the people of Mosul will be free," he said.
The coalition has come under criticism following an air strike in west Mosul last month that took a heavy toll on civilians, a strike it admitted may have been its own.
"Every strike that we conduct, we conduct using precision-guided munitions. Every strike that we conduct is coordinated directly with the Iraqi security forces," Dorrian said.
"We are very careful. We never, ever target civilians," he added.
But even if IS members are targeted, the fact that they are operating in areas still home to large numbers of residents means that civilians can easily still end up the victims.
IS still controls the large towns of Hawijah and Tal Afar as well as remote areas along the border with Syria in western Iraq. It also holds the city of Raqa and other areas in Syria.