BAGHDAD: A top Iraqi general said the army may permit Islamic State militants to flee the offensive on Falluja, but he expected most of them would fight to the end and predicted they faced an internal uprising in the northern city of Mosul.

Troops recaptured Falluja's municipal building on Friday, although the ultra-hardline militants are still holed up in several districts and have left many streets and buildings laced with explosives.

The military has made quick progress in the city, an hour's drive from Baghdad, prompting the exodus of more than 68,000 residents.

Asked if government forces would allow militants a path out of the city to avoid intense clashes in built-up areas that could kill remaining civilians and destroy infrastructure, General Talib Shaghati Mshari al-Kenani said they would try.

"But the Daesh terrorists in Falluja will detonate suicide bombs to kill innocent Iraqis, believing they will enter heaven by doing so," he told Reuters in an interview on Thursday, using an Arabic acronym for Islamic State.

Kenani, who heads the Joint Operations Command waging Iraq's war against Islamic State in coordination with a U.S.-led coalition, was speaking at his Baghdad office inside a compound guarded by black-clad special forces commandos.

In previous offensives, Iraqi forces have often left a way out for the insurgents to escape, but after losing nearly half the Iraqi territory they seized in 2014 and major transit routes including to neighbouring Syria, their options are narrowing.

Government troops launched a major operation with coalition air support on May 23 to retake Falluja, a bastion of the Sunni Muslim insurgency against US forces that toppled Saddam Hussein, a Sunni, in 2003, and later Shi'ite-led governments.

The participation of Iranian-backed Shi'ite militias alongside the Iraqi army raised fears of sectarian killings, and authorities are already investigating allegations that militiamen executed dozens of Sunni men fleeing the city.

Kenani said the military plan for operations inside Falluja proper did not include a role for the militias, grouped under a government umbrella called the Hashid Shaabi.

He said the Hashid would likely not be needed either in the campaign for the Islamic State stronghold of Mosul, a predominately Sunni city which Prime Minister Haider al-Abadi has pledged to retake this year.

"The tribal Hashid, local police and volunteers from the Sunni areas occupied by Daesh will help to hold land. No need for additional forces from outside the area," he said, in an apparent reference to Shi'ite militiamen.

HOPES FOR MOSUL UPRISING

Falluja is seen as a launchpad for recent Islamic State (IS) bombings in the capital, making the offensive a crucial part of the government's campaign to improve security, though U.S. allies would prefer to concentrate on Mosul.

The army is pushing about 60 kilometres (40 miles) south of Mosul towards Qayara, where an airfield could serve as a staging ground for the future offensive, but progress has been faltering.

Kenani said the military had information that residents inside Mosul, estimated at more than one million, were preparing to rise up against the insurgents and was in contact with them to synchronise such action with an external military assault.

"Cooperation and coordination with Mosul residents will contribute in a big way to the armed forces in liberating the city from Daesh," he said, but gave no details.

Groups inside Mosul have reportedly scrawled anti-Islamic State graffiti in public places and attacked militants at checkpoints, but there have not been widespread acts of resistance.

Kenani, who is also commander of Iraq's elite counter-terrorism service (CTS) which has spearheaded battles against Islamic State for more than two years, said he expected special forces to remain in the vanguard against pockets of Islamist militants once the government regains control.

"These sorts of operations which happen in densely populated areas don't require regular armed forces but rather special operations units which are small and adaptable."

The roughly 10,000 members of CTS, established a decade ago with support from the US forces, are considered the best-trained and -equipped fighters in Iraq.

Kenani said they would be needed for the foreseeable future.