An Iraqi military parade in Baghdad's heavily fortified Green Zone celebrated final victory over Islamic State on Sunday, with Prime Minister Haider al-Abadi looking on as troops marched in formation, their bodies spelling 'victory day' in Arabic.

Abadi, who is also commander-in-chief of the armed forces, listened solemnly to Quranic verses from a chapter titled al-Nasr, meaning victory.

Iraqi forces recaptured the last areas still under Islamic State control along the border with Syria on Saturday and secured the western desert, marking the end of the war against the militants three years after they had captured about a third of Iraq's territory.

The forces fighting Islamic State in Iraq and Syria now expect a new phase of guerrilla warfare.

Watching the parade on Sunday, state television showed Abadi sat on a throne-like chair placed between two Iraqi flags with the country's official seal behind him, and with all other officials sat at a distance from him.

Abadi declared December 10 would be an annual national holiday. Fighter jets were seen and heard flying over Baghdad's skies.

An announcer introduced various factions who took on Islamic State as troops marched, tanks rolled by and helicopters hovered, all brandishing Iraqi flags as Abadi stood up and waved.

Those who fought were drawn from the army, air force, federal and local police, elite counter-terrorism forces, as well as Shi'ite and Sunni paramilitaries and Kurdish Peshmerga fighters. They received key air support from a US-led global coalition.

In his victory speech, delivered on Saturday, Abadi did not mention the Peshmerga, who played a big part in the fight against Islamic State.

The central government in Baghdad is in conflict with the semi-autonomous Kurdistan Regional Government after the latter unilaterally held an independence referendum in September.

Instead Abadi hailed the Iranian-trained and backed Popular Mobilisation Forces (PMF), a group of Shi'ite militias, many of whom are loyal to Iran.

He also said that the state should have a legitimate monopoly on arms, however. Disarming the PMF is seen as Abadi's greatest challenge after Islamic State's defeat.

The man who many saw as weak and ineffectual when he took over in 2014 from a predecessor who was blamed for the Islamic State takeover now heads towards an election next year as the commander who freed Iraqi lands.

Or as one Western diplomat described him - 'the most popular man in Iraq.'