The Islamic State group on Sunday pulled its fighters out of Rutba, a desert town in the western Iraqi province of Anbar, an army general and the mayor said.

The pullout, if confirmed, would be a rare case of the militants abandoning a position under no massive miliary pressure and suggests a manpower crisis in the organisation.

"Daesh (IS group) has completely pulled out of Rutba and gone towards Al-Qaim," a major general told AFP, referring to a jihadist bastion on the border with Syria, further north in Anbar.

"Daesh's armed men started pulling out last night and completed their withdrawal this morning," the senior officer said, speaking on condition of anonymity. "Rutba is now free of Daesh."

The mayor of the isolated town, which lies about 390 kilometres (245 miles) west of Baghdad on the road to Jordan, confirmed that IS group had withdrawn.

"Daesh has pulled out. They have no armed men there now," Imad Ahmed said.

"This withdrawal looks real, a consequence of their losses in Anbar, notably the retaking by the security forces of Ramadi, of areas east of Ramadi and the progress towards Hit," he said.

After launching a final push against IS group in the provincial capital Ramadi late last year, Iraq's security forces established full control over the city last month.

They have since been securing areas east of Ramadi, further isolating the jihadist stronghold of Fallujah, which lies only 50 kilometres (30 miles) west of Baghdad.

The security forces are also currently working their way up the Euphrates, west of Ramadi, with a view to retaking the town of Hit.

"It cannot be ruled out however that Daesh is pulling out to try to lure out sleeper cells among the population cooperating with the security forces," the mayor said.

"We have warned the residents that this could be a trick... and asked the Iraqi security forces to come and retake control of the area," he said.

The major general said any operation in the Rutba needed the approval of Prime Minister Haider al-Abadi and sufficient time to plan.

Raja Barakat, a member of Anbar provincial council's security committee, confirmed the Rutba pullout and said IS group had also been pulling some of its forces from Hit.

"It was not just from Rutba but also from Hit after their fighters shaved their beards to slip out," he said.

"But in Hit, it's not a complete pullout, some Daesh fighters remain," Barakat said.

He said that the IS group fighters who withdrew from Hit moved through the desert towards Baiji, to the northeast, and towards Al-Qaim, to the northwest.

The US-led coalition that has been carrying air strikes against IS group for more than a year and a half has said that the miltant group was stretched increasingly thin.

Iraqi forces have in recent weeks been attempting to flush out miltants from vast areas around Lake Tharthar, which straddles Anbar and the province of Salaheddin.

In several of its strongholds, IS group is reported to have forcibly recruited children to man checkpoints as it sends adult males to combat.

*This story was edited by Ahram Online.