The tightening siege of Fallujah is trapping jihadists in the city and Iraqi fighters predict that the Islamic State group could make a longer and bloodier last stand than usual.

By the time Iraqi forces picked their way through a dense network of roadside bombs and booby traps and reached the hearts of Ramadi and Tikrit last year, most enemy fighters had vanished.

While many of IS's most senior commanders, including the foreign leaders, are reported to have fled Fallujah, Iraqi troops expect to encounter more than a small residual IS force.

As the elite counter-terrorism service (CTS) began to creep into Fallujah, the tens of thousands of other forces who have been shaping the battlefield finished sealing off the city.

On Monday, a force led by the Hashed al-Shaabi paramilitary force cut off Fallujah from Jazirat al-Khaldiyah, an area to the west which IS has been transiting through to reach its other positions across the country.

"This time is different... because now they have no routes along which to bring in supplies and reinforcements or to escape," said Mohammed Salem, a senior Hashed officer involved in the operation near Saqlawiya.

"It could result in this battle dragging on though," he said.

Saif Salem, a member of the Furqat Imam Ali Shiite militia, just returned from the front line, caked in yellow dust from head to toe.

"Daesh (IS) are besieged. They can't escape at this stage. Their only option is a suicide holdout," said the young fighter from Najaf.

"This is what we face now but our morale is high and theirs is fragile. They want to drag us into the city in order to try to leave by blending in with the population," Salem said.

Abu Wahib, the top IS commander for the whole province of Anbar, in which Fallujah is located, was killed in a US-led coalition air strike on May 6.

A few days later, a commander described as the group's military leader in Fallujah, Maher al-Bilawi, was also killed.

- IS 'not that strong' -

A resident in the city contacted by phone told AFP there was sense of panic among jihadists, who have been rounding up men and ever younger boys, presumably as forced recruits to beef up their defence of Fallujah.

Besieged or not, David Witty, a retired US army special forces colonel, said he expected IS, a Sunni extremist group, to put up more of a fight than it did for other cities.

"After all, this place has been a symbol since 2004 of Sunni resistance to both the Baghdad government and the US," he said.

"If IS is unable to retain (Fallujah), it could be a significant psychological blow to the organisation," said Witty, a former advisor to CTS.

It was in Fallujah in November 2004 that Al-Qaeda in Iraq, a previous incarnation of the Islamic State group, inflicted some of the worst losses on the US military since the Vietnam War.

It took 10,000 highly trained US forces equipped with the best technology more than six weeks to gain the upper hand back then.

As the jihadists lost areas around Fallujah and elsewhere in Anbar in recent weeks, some fighters have regrouped inside their old stronghold.

Estimates vary but at least 1,000 IS fighters are believed to be hunkering down inside Fallujah, including in a network of tunnels, waiting for Iraqi forces to walk into the mousetrap.

By the time Iraqi forces had fully retaken Ramadi, the capital of Anbar, early this year, much of the city had been levelled.

Yahya Rasool, spokesman of the Joint Operations Command in charge of the fight against IS, does not believe IS fighters are willing or able to make a heroic last stand.

But there are an estimated 50,000 civilians left in Fallujah and that could also be a slowing factor in the battle, he said.

"Daesh are not that strong," he told AFP. "Their spirit is broken, but the priority that was made clear to us in the armed forces is to preserve the lives of civilians and the city's infrastructure."