Iraq's army declared victory over ISIS fighters on Sunday after taking control of a government complex in central Ramadi — the last stronghold in the city held by the jihadist group, according to a military spokesperson.

It is being hailed as the first major triumph for the U.S.-trained force since it collapsed in the face of an assault by the militants 18 months ago.

"By controlling the complex this means that they have been defeated in Ramadi," said Sabah al-Numani, a spokesman for the force leading the fight on the government side.

"The next step is to clear pockets that could exist here or there in the city."

The Iraqi military claim a major victory in the fight against ISIS, Derek Stoffel reports from Jerusalem 2:53

"The complex is under our complete control, there is no presence whatsoever of Daesh fighters in the complex," he told Reuters, using a derogatory Arabic acronym of Islamic State.

Recapturing Ramadi, which fell to the militants in May, would be one of the most significant victories for Iraq's armed forces since Islamic State swept across a third of the country in 2014.

Earlier Sunday, Gen. Ismail al-Mahlawi had said troops may "need days" to regain control over the complex in Anbar province. He said the advance was being hampered by Islamic State suicide bombers, snipers and booby traps.

Iraqi security forces on Saturday blew up a car belonging to a suicide bomber with Islamic State group in the Huz neighbourhood of downtown Ramadi, 115 kilometres west of Baghdad. They reached the area at dawn as part of a major offensive aimed at dislodging the Islamic State militia from the western Iraqi city. (Osama Sami/Associated Press)

On Saturday, joint operations command spokesman Brig. Yahya Rasool said coalition airstrikes have helped to detonate car bombs and booby-trapped houses.

The Iraqi government has said that Ramadi, if captured, would be handed over to the local police and to a Sunni tribal force.

Ramadi was ISIS's biggest prize of 2015, abandoned by government forces in May in a major setback for Baghdad and for the Iraqi troops that have been trained mostly by the U.S. since the overthrow of Saddam Hussein in 2003.

ISIS is blamed for destroying this bridge in Ramadi to thwart the advance of Iraqi troops. (Associated Press)

After Ramadi, the army plans to move to retake the northern city of Mosul, the biggest population centre under ISIS control in Iraq and Syria.

The extremists still control large swaths of land in western and northern Iraq and in neighbouring Syria. The Islamic State in Iraq and Syria (ISIS) has declared a self-styled caliphate on the territory under its control.

After overrunning Ramadi, ISIS destroyed all the bridges around the city. It also demolished the Anbar operations command centre and fanned out into the city's residential areas to set up less conspicuous centres of command.