"We declare that Daesh's presence has receded in the cities and provinces of Iraq," Saad al-Hadithi said in televised comments.
"They were occupying 40 percent of Iraq's territory but now only 14 percent is under their control," he said.
The jihadist organisation launched a massive offensive in Iraq in June 2014 and conquered swathes of territory. Its stopped advancing before it could reach the capital Baghdad.
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A counter-offensive was subsequently launched with heavy involvement from Tehran-backed Shiite militia groups and a coalition of military powers led by the United States.
IS has since lost several key cities, such as Tikrit and Ramadi. The "caliphate" it proclaimed nearly two years ago has been shrinking steadily for a year.
Iraqi security forces are currently battling IS on several fronts, including in the provinces of Anbar and Nineveh in a bid to retake Fallujah and Mosul, the group's two major remaining hubs in the country.
IS has nonetheless retained the ability to strike in Iraqi cities by carrying deadly suicide bombings, such as the three attacks that killed at least 86 people in Baghdad on Wednesday.
Hadithi went on state television hours after Wednesday's first attack, a huge car bomb blast in a busy market area of the Sadr City neighbourhood that killed at least 64 people.