The fall of Ramadi has scuppered Iraqi Prime Minister Haider al-Abadi's efforts to build a credible cross-sectarian force to fight the Islamic State group, analysts said Monday.

The commander-in-chief had been keen, with strong US support, to make Anbar province the place where Sunni tribal forces under his command would prove their worth.

The first unit of 1,180 Sunni tribal fighters fully integrated into the Popular Mobilisation units (Hashed al-Shaabi) was to graduate Monday at Habbaniyah base, east of Ramadi.

Now that base is teeming with the Hashed's Shiite fighters Abadi reluctantly called in after the Islamic State group's capture of Ramadi sparked a chaotic army retreat.

"It's a miscalculation from the commander in-chief (Abadi)," Iraqi analyst Ihsan al-Shammari said. "He wanted to give the US a place and the tribesmen a bigger contribution."

"While you're at war with extremist groups, you can't make political calculations or seek to balance international or regional powers. The most important is not to lose ground," he said.

Sunday's defeat in Ramadi was Baghdad's worst military setback since an IS-led offensive in June 2014 saw the army collapse and the government lose key cities and vast swathes of land.

The Hashed al-Shaabi is an umbrella organisation meant to give a legal status and centralised command to powerful Iran-backed Shiite militia groups and volunteers that have done much of the heavy lifting in Baghdad's anti-IS fightback so far.

Abadi has strived to change the organisation's image as a sectarian entity, many of whose components have been accused of abuses against the Sunni population during previous battles.

But while Hashed fighters are nominally under Abadi's control, he has little influence over them, said London-based analyst Ayham Kamel, director for the Middle East and North Africa at the Eurasia Group.

"Today is the first real challenge, not just a security challenge but on the political level too, to Abadi's authority," he said.

Abadi's own political camp is divided and many within his own party, led by his predecessor Nuri al-Maliki, have opposed his security strategy.

- Abadi mistakes -

The main groups in Hashed al-Shaabi made no secret of their displeasure with Abadi's choices so far.

"The government's insistence on following the American vision made us go into Anbar to defend the people of Anbar and not let the situation drag on any longer," Jaafar al-Husseini, a spokesman for Ketaeb Hezbollah, one of Iraq's leading Shiite militias, told AFP.

The Badr organisation, another leading Shiite paramilitary group which holds several portfolios in Abadi's government, also argued that the loss of Ramadi should have been avoided.

"We will take part in the battles of Anbar based on the official decision of the prime minister, even though it was over a month late," Moeen al-Kadhimi, a Badr leader, said.

Ayham Kamel, the analyst, argued that Abadi, who took office in September, tried to achieve too much by attempting the kind of security reforms that usually take years while accommodating his Iranian and US allies.

"Abadi has made big mistakes... He really constrained himself in terms of short-term strategy. Iraq was stuck without an active fighting force," he said.

The result is what Tehran's enemies had dreaded: Iran-backed Shiite forces operating deep in Iraq's Sunni heartland, in a province that has borders with Jordan and Saudi Arabia.

Anbar was considered part of the US sphere of influence. US troops have much experience there having fought the toughest battles of their eight-year occupation in the province.

They currently have hundreds of military advisers based at Al-Asad base, west of Ramadi, and conduct daily air strikes against IS in the province.

Control over Anbar is seen by the Shiite groups as key to securing the holiest Shiite shrines in Iraq -- in Baghdad, Najaf and particularly in Karbala.

In a rare recorded speech, which has yet to be authenticated, Saddam Hussein's elusive deputy Izzat Ibrahim al-Duri purportedly accused Tehran of seeking to expand its influence beyond its natural ambit.

"Iran is rushing to swallow Iraq to start its main battle with the (Arab) nation, with the Gulf countries, with Saudi Arabia," he said in the speech, which was released on Friday.

The presence of Iran-backed paramilitary in one of its bastions will also be like a red rag to a bull for IS, whose leader Abu Bakr al-Baghdadi put special emphasis on Anbar in his own audio message, released a day earlier.