Iraqi soldiers have discovered two shallow graves containing the bodies of people executed by the Islamic State group in the western desert town of Rutba, officials said Thursday.

"The Iraqi army found two mass graves in Rutba containing the bodies of members of the security forces and of civilians," a captain in the army's 1st division told AFP.

He said the first indications suggested the victims had been executed by IS when the jihadist group took control of the town in mid-2014.

Rutba, a small town of significant strategic value, lies on the road to Jordan, about 390 kilometres (245 miles) west of Baghdad.

The mayor of the town, which was retaken from IS in May last year, said one grave was found on a plot in a central neighbourhood that had been used to dump hospital waste while the other was located on Rutba's southern edge.

"The bodies we have seen have bullet impacts... We don't know the exact number of bodies because we are leaving this work to a forensic team but we expect there are about 25," Imad Meshaal said.

Rutba is very isolated in the desert of Anbar, a vast western province that has long been a Sunni insurgent stronghold and has borders with Saudi Arabia, Jordan and Syria.

IS militants have attacked the town several times since the security forces retook control of it.

Dozens of mass graves have been found across areas of Iraq that IS seized in 2014 and have since been retaken by the security forces.