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 officialoversight, 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