Iraq's premier said Wednesday that the country's "next battle" is to retake Anbar province from the Islamic State jihadist group, his most direct statement yet on Baghdad's target after Tikrit.

"Our next stand and battle will be here in the land of Anbar to completely liberate it," Haider al-Abadi said from a base in the province west of Baghdad, according to his office.

He was visiting Anbar to "check on preparations" for the upcoming military campaign.

Abadi announced last week that Iraqi forces retook the city of Tikrit from IS, in Baghdad's biggest victory to date over militants who overran large parts of the country last June.

It was unclear if the next target would be Nineveh, IS's main stronghold in Iraq and the first province to fall last year, or Anbar, a massive desert province stretching from the borders with Syria, Jordan and Saudi Arabia to the western approach to Baghdad.

While IS has gained further ground in Anbar since June, the government's loss of territory in the province predates the jihadist offensive by six months.

Security forces dismantled a key anti-government protest camp near provincial capital Ramadi in late 2013, sparking a crisis that saw anti-government fighters take parts of that city and all of Fallujah, to its east.

Iraqi forces have battled IS for months but made little progress in the massive province, where the government only controls pockets scattered across territory broadly under IS control, making any wide operation a logistical challenge.

Iraqi soldiers and police along with Popular Mobilisation units -- paramilitary forces that are dominated by Iran-backed Shiite militias -- have regained signficant territory from IS north of the capital.

They retook Diyala province, then fought a month-long battle for Tikrit in neighbouring Salaheddin.

- Lessons from Tikrit -

Though Tikrit was a significant success for the government, it also highlighted problems facing Iraqi forces on other fronts, including Anbar.

One is the difficulty of rooting out entrenched jihadists.

While Abadi said Tikrit has been retaken, the interior ministry said there was fighting against IS holdouts in the city as recently as Wednesday, over a week later.

The myriad forces involved in anti-IS efforts pose a challenge for command and control, especially when militiamen are disparaging the army and the army is suspicious of the militias, as was the case during the Tikrit operation.

"There was a very important lesson in the battle of Tikrit," Defence Minister Khaled al-Obeidi told a news conference in the Jordanian capital Amman.

"Disciplined national forces that will fight under the command of the army are those that will participate in future battles," he said, indicating some unnamed groups had not met that standard.

Some Shiite militiamen looted stores in central Tikrit, while Obeidi said that "groups" numbering some 2,000 people entered the city after it was retaken and "began vandalising and burning."

Obeidi said 67 houses and 85 shops were burned, terming this "unacceptable", while saying that the toll for the city could ultimately have been worse.

Tensions between Iranian-backed militias -- which are the largest and most effective -- and the US-led coalition are also an issue, and both are playing a role in Anbar.

Washington made clear that it did not want Iranian-backed groups involved in Tikrit, while they said the same of the US, freezing their offensive operations after the strikes began.

It also took a month for Iraqi forces to retake Tikrit -- a relatively small city that IS seeded with bombs and defended with snipers and suicide bombers.

Recapturing the vastly larger area of Anbar, where militants have had even longer to prepare their defences, will be a major challenge.