Iraqi Prime Minister Haider al-Abadi visited the western city of Ramadi on Tuesday, a day after the army declared it "liberated" from Islamic State militants.

A photograph on his official Facebook page showed al-Abadi, accompanied by armed guards and military officers, placing an Iraqi flag on a riverbank

Another picture showed him crossing what appeared to be the pontoon bridge erected by Iraqi forces to enter Ramadi after Islamic State blew up the city's bridges.

The premier toured areas of the city recaptured from the jihadists and spoke to soldiers who had taken part in the operation, his office said.

Security forces were meanwhile moving to take control of remaining areas of the city, officials said.

"The military will be carrying out mopping-up operations in Ramadi and moving to other areas to liberate them and recapture them from the terrorists," Anbar police spokesman Yasser al-Dulaimi said.

Al-Dulaimi said government forces would shortly enter the Thila district near the government compound in the city centre where troops raised the Iraqi flag on Monday, shortly before the army declared victory.

Most of the Islamic State militants in the area had probably fled the city already for their stronghold in Fallujah nearer to Baghdad, al-Dulaimi said.

The recapture of Ramadi, which fell to Islamic State in May, is the most significant advance by government forces since they took the northern city of Tikrit at the end of March.

A map posted online by the spokesman for the US-led coalition against Islamic State suggested that, despite al-Abadi's declaration of victory, there was some way still to go before the city was fully secured.

The map posted by Colonel Steve Warren showed areas cleared by Iraqi security forces in green. They included the government complex where troops raised the Iraqi flag on Monday, but much of the rest of the city centre was not marked as cleared.

The extent of the destruction in Ramadi was becoming clearer on Tuesday, with provincial council member Udhal al-Fahdawi saying 80 per cent of the city had been destroyed.

The council would work to ensure that civilians could return home, but mines and explosives laid by the jihadists to hamper the advance of government forces would have to be cleared first, al-Fahdawi said.

More than a quarter of a million people have fled the violence in Ramadi, according to the International Organization for Migration.

Sources inside the city said only about 120-130 civilians, who had been unable to leave, were thought to remain there as of Tuesday.

Al-Abadi on Monday hailed the recapture of Ramadi as a major victory, vowing that 2016 would see the jihadists "rooted out" of Iraq with an assault on their main stronghold of Mosul in the north of the country.

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