BAGHDAD (Reuters, AFP) - Iraqi elite forces recaptured the last remaining district held by Islamic State militants in the city of Falluja on Sunday (June 26) and the general commanding the operation declared the battle complete.

Prime Minister Haider al-Abadi claimed victory over Islamic State in Falluja more than a week ago but fighting continued inside the city, including in the Golan district.

"We announce from this place in central Golan district that it has been cleaned by the counter terrorism service and we convey the good news to the Iraqi people that the battle of Falluja is over," Lieutenant General Abdul Wahab al-Saidi told state TV.

At least 1,800 militants were killed in the month-long operation to retake Falluja, he said.

The elite 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 ISIS.

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

A spokesman for the Joint Operations Command coordinating the fight against ISIS said some jihadist pockets remained northwest of Fallujah. "We still have an ongoing fight northwest of Fallujah. We never made central Fallujah the ultimate goal of our operation... the aim is to clear the whole area," the spokesman said.

The Iraqi security forces launched a major offensive on May 22-23 to retake Fallujah, one of ISIS's most emblematic bastions, which lies only 50km west of Baghdad.