Iraq's counter-terrorism forces deployed on the edge of Fallujah Saturday 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, a bastion of the 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, told AFP.

"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 kilometres (30 miles) west of Baghdad, is one of the two remaining major Iraqi cities 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," Noman said.

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

The aim is 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.

Humanitarian players have expressed concern over the fate of an estimated 50,000 civilians thought to be trapped inside the city.

"We are receiving hundreds of displaced Iraqis from the outskirts of Fallujah who are totally exhausted, afraid and hungry," Nasr Muflahi, country director for the Norwegian Refugee Council (NRC), said in a statement.

"Thousands more remain trapped in the centre of Fallujah, cut off from aid and any form of protection," he said.

NRC said only 249 families (around 1,500 people) they knew of had managed to flee the Fallujah area since the launch of military operations nearly a week ago.

It said all but one family were from outlying areas, not the city centre.

The estimated 1,000 jihadists still ruling the city are suspected of using civilians as human shields but the UN's refugee agency also said that Iraqi forces had blocked supply routes, thus preventing people from leaving.