Iraqi security forces advanced Tuesday into the centre of Ramadi for a final push aimed at retaking the city they lost to the Islamic State group in May, officials said.

"We went into the centre of Ramadi from several fronts and we began purging residential areas," said Sabah al-Noman, spokesman of the elite Iraqi counter-terrorism service.

"The city will be cleared in the coming 72 hours," he said.

"We did not face strong resistance, only snipers and suicide bombers and this is a tactic we expected," Noman told AFP.

The fresh push was launched on Monday night and aims to result in the full recapture of Ramadi, the capital of Anbar province in western Iraq.

Footage on state TV channel Iraqiya showed soldiers driving down the deserted streets of the bombed-out city, entering homes with caution to detect possible booby traps and retrieving shells and rockets from abandoned IS positions.

The fighting in Ramadi is led by the elite counter-terrorism force, backed by US-led coalition air strikes and also supported by the police, army and Sunni tribes opposed to the jihadists.

IS has lost several key towns in Iraq since Baghdad and the autonomous Kurdish region in the north started fighting back following the jihadist group's devastating offensive 18 months ago.

The Shiite-dominated Hashed al-Shaabi paramilitary forces were heavily involved in battles that led to the recapture of towns such as Tikrit and Baiji, but they have remained on the fringes in the battle for the Sunni city of Ramadi.

- Government compound -

Retaking the city, an insurgent bastion that saw some of the deadliest fighting against US troops a decade ago, would be the Iraqi federal forces' most significant victory so far.

"We built temporary bridges on the Euphrates and our forces were able to cross the river to enter residential areas and gain access to the city centre," a brigadier general said, speaking on condition of anonymity.

IS fighters have had plenty of time to dig in since they took full control of Ramadi on May 17 after blitzing government forces with wave after wave of car and truck bomb attacks.

The jihadists built tunnels to move without being exposed to the coalition's daily raids, but their supply lines have been gradually severed and military officials estimated last week there were no more than 300 fighters left in the city.

The breakthrough came earlier this month when counter-terrorism forces broke down IS defences and retook the key southwestern neighbourhood of Al-Tameem.

After beefing up their new positions, Iraqi military leaders had said a final push was imminent and leaflets urging the population to flee were dropped over the weekend.

"The distance between our forces and the governmental compound, which is located in the central district of Hoz, is less than a kilometre" or 500 yards, said the brigadier general.

- Civilians fleeing -

The provincial headquarters is believed to be one of the main IS bases in the city, and was at the heart of deadly fighting earlier this year.

According to another military official, speaking on condition of anonymity because he is not authorised to talk to the press, 15 families had managed to escape from Hoz in the past 24 hours.

"They were able to flee the lockdown imposed by Daesh on civilians and they found shelter with the army on the southern side of the city," he said, using an Arabic acronym for IS.

The senior officer said the civilians were mostly children, women and elderly men who were screened and then taken to a safe area on the edge of Ramadi.

Defence Minister Khaled al-Obeidi and other officials said in recent days they believed there were still a few civilians in Ramadi being used as human shields by IS.

The coalition said its aircraft had been carrying out six strikes a day on IS targets in the Ramadi area for the past month.

"The fall of Ramadi is inevitable, the end is coming but... it's gonna be a tough fight," coalition spokesman Steve Warren told US reporters in a videoconference from Baghdad.

He also said there were at least thousands of civilians left inside Ramadi, "possibly tens of thousands".

A victory in Ramadi would leave Mosul, Tal Afar and Fallujah as the only major Iraqi cities still in IS hands and further undermine the group's claim that the caliphate it proclaimed last year is expanding.

Obeidi has said successive operations have shrunk the area controlled by IS from nearly 40 percent of Iraq last year to 17 percent.