Shiite militias backed by the Iraqi army are committing war crimes against civilians in their fightback against the Islamic State jihadist group, rights watchdog Amnesty International said Tuesday.

It accused the Baghdad government of supporting and arming groups of Shiite fighters who have carried out a string of kidnappings and killings against Sunni civilians in response to IS's lightning capture of swathes of Iraqi territory in June.

Amnesty said it had seen evidence of "scores" of "deliberate execution style killings" against Sunnis across Iraq as well as Sunni families having to pay tens of thousands of dollars to free abducted relatives.

Many of those kidnapped are still missing and some were killed even after their families paid hefty ransoms to secure their release, the group said in a report.

The watchdog called on the government of newly-installed Prime Minister Haidar al-Abadi to rein in the scores of militias targeting civilians across Iraq.

"By granting its blessing to militias who routinely commit such abhorrent abuses, the Iraqi government is sanctioning war crimes and fuelling a dangerous cycle of sectarian violence that is tearing the country apart," said Donatella Rovera, Amnesty International's senior crisis response adviser.

The Sunni extremist fighters of IS seized control of swathes of territory in a June offensive that saw many Iraqi army units abandon their posts.

The group now controls large parts of western and northern Iraq, including the country's second city of Mosul.

Army missions to regain ground are often conducted alongside allied groups of Shiite fighters, raising fears Iraq is returning to the deadly sectarian violence of the mid-2000s.

"The growing power of Shiite militias has contributed to an overall deterioration in security and an atmosphere of lawlessness," Amnesty said.

Rights organisations accuse the IS group of widespread abuses, including the targeting of civilians in suicide bomb attacks and carrying out executions on captured soldiers, activists and journalists.

The group boasted on Monday it had revived slavery, providing its fighters with minority Yazidi women and children taken from northern Iraq as spoils of war.

Amnesty accused Shiite armed groups of using the battle against IS as a pretext for carrying out "revenge" attacks on members of the Sunni community.

"Shiite militias are ruthlessly targeting Sunni civilians on a sectarian basis under the guise of fighting terrorism," it said.

- 'Government must investigate' -

The watchdog also accused Iraqi government forces of serious rights violations, including evidence of "torture and ill-treatment of detainees, as well as deaths in custody" of inmates held on terror charges.

It said the body of a lawyer and father of two young children who had died in custody showed bruises and may have been electrocuted by guards.

Another man was given electric shocks and threatened "with rape with a stick" before he was released without charge, Amnesty added.

"Successive Iraqi governments have displayed a callous disregard for fundamental human rights principles," Rovera said.

"The new government must now change course and put in place effective mechanisms to investigate abuses."