Shia militias have abducted and murdered scores of Sunni civilians in Iraq in crimes committed in retribution against the actions of ISIL, according to a new report by Amnesty International.

The London-based rights group on Tuesday published what it said was evidence that Shia militias abducted civilians in Baghdad, Samarra and Kirkuk, and killed them even if families paid tens of thousands of dollars in ransom.

The Amnesty report, Absolute Impunity: Militia Rule in Iraq, said scores of unidentified bodies had been discovered handcuffed and with gunshot wounds, indicating a pattern of deliberate killings.

The group called on the Iraqi government, which has armed and encouraged militias including the Badr brigades and the Mehdi army, to fight ISIL, to hold them to account.

Militias operate outside any legal framework and without official oversight, and had contributed to a deterioration in security and to the increasing lawlessness in Iraq, Amnesty said.

"Shia militias are ruthlessly targeting Sunni civilians on a sectarian basis under the guise of fighting terrorism, in an apparent bid to punish Sunnis for the rise of ISIL and for its heinous crimes," Donatella Rovera, Amnesty's senior crisis response adviser, said.

"By failing to hold militias accountable for war crimes and other gross human rights abuses the Iraqi authorities have effectively granted them free rein to go on the rampage against Sunnis. The new Iraqi government of Prime Minister Haider al-Abbadi must act now to rein in the militias and establish the rule of law."

'Evidence of torture'

The Amnesty document included evidence from relatives of those who had gone missing or were killed.

The new government must now change course and put in place effective mechanisms to investigate abuses by Shia militias and Iraqi forces and hold accountable those responsible Donatella Rovera,

Amnesty International

It reported that one family had paid $60,000 to have a family member released, only to find his body two weeks later in a Baghdad morgue, his head crushed and his hands cuffed.

Amnesty also accused Iraqi government forces of serious human rights violations, presenting what it said was evidence of torture and ill-treatment of prisoners, and deaths in custody of Sunni men held under the 2005 anti-terrorism law.

It cited one example of a 33-year-old lawyer who died in custody, his body showing open wounds and burns consistent with the application of electric shocks.

Another man was held for five months and tortured with electric shocks and threatened with rape before being released without charge.

"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 by Shia militias and Iraqi forces and hold accountable those responsible."

In response, Naeem Al-Aboudi, the spokeman of Aasab Ahl Haq, a Shia paramilitary group, criticised the Amnesty report, calling it "an attempt to downgrade our gains and accomplishments so far in the fight against ISIL by supporting the Iraqi forces."

"We had fought and won over ISIL in Shia and Sunni areas and while doing so we had not violated any human rights."