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Iraqi forces recaptured the city of Fallujah from Islamic State militants just a month after launching an operation against the group, the army announced on Sunday.

Elite Iraqi forces "fully liberated" the city and secured full control more than two years since it was captured by IS.

"Today the commander of Fallujah operations Lieutenant General Abdelwahab al-Saadi announced that the city of Fallujah had been cleared after counter-terrorism forces (CTS) took control of the Jolan neighbourhood," the force's spokesman, Sabah al-Noman, told AFP.

"Jolan was Daesh's last stronghold in the city and Fallujah is now free of the threat posed by Daesh terrorists," he said, using an Arab acronym for IS.

"It did not take more than two hours for CTS to retake Jolan. Daesh did not fire a single bullet," Noman said, adding that this is proof that "Daesh was defeated even before our forces got there."

On Thursday, forces closed in to flush out the last pockets of militants from the Islamic State group in Fallujah after liberating more than 80 percent of the city.

British Army Major General Douglas Chalmers, a spokesman for the US-led coalition on Thursday said the fight to get into the city "was probably some of the fiercest I think I've probably seen."

Fallujah, which lies 50 kilometres (30 miles) west of Baghdad, was the first city to fall out of government control in 2014, months before IS swept across Iraq and declared its "caliphate".

A major offensive including several factions was launched on May 22 to recapture the city from the Islamic State.