Iraq's counter-terrorism forces have deployed on the edge of Fallujah for the first time since an operation was launched to retake the jihadist-held city, top commanders said.

The Counter-Terrorism Service (CTS), Iraq's best-trained and most battle-tested fighting unit, moved into position on the boundaries of Fallujah today, a bastion of the so-called Islamic State group.

"CTS forces, Anbar emergency police and tribal fighters... reached Tareq and Mazraa camps," south and east of Fallujah, Abdelwahab al-Saadi, the top commander in charge of the Fallujah operation, said.

"These forces will break into Fallujah in the next few hours to liberate it from Daesh," he said, using an acronym for IS.

Fallujah, which lies just 50 kms west of Baghdad, is one of the two remaining major Iraqi cities (along with Mosul) still controlled by IS.

CTS spokesman Sabah al-Noman confirmed the deployment but would not comment on the timing of an assault.

"CTS forces moved to Fallujah to take part in clearing the city from within. The operation is shifting to urban warfare after Iraqi forces completed the siege of the city," he said.

"CTS forces will break into the city, that's what they specialise in," Mr Noman said.

Tens of thousands of Iraqi forces, including the Hashed al-Shaabi umbrella group dominated by Tehran-backed Shi'ite militias, began a huge operation on 22-23 May.

The aim is to retake Fallujah, the first city to fall out of government control even before IS swept through Iraq's Sunni Arab heartland in June 2014, and one of IS's most iconic strongholds.

The Hashed al-Shaabi forces ('Population Mobilisation' in Arabic), as well as army and police forces have so far focused their efforts on areas east of Fallujah, without entering the city proper.

The CTS led the assault on several other major towns, cities and strategic sites across the country that were retaken from the jihadists over the past two years.

Their involvement marks a new phase in the Fallujah operation.