Militias fighting alongside Iraqi troops against Daesh are committing war crimes using weapons provided to the Iraqi military by the United States, Europe, Russia and Iran, Amnesty International said on Thursday.

The rights group said that predominantly Iran-backed militias, known collective as the Hashdi al-Shaabi, were using weapons from Iraqi military stockpiles to commit war crimes including enforced disappearances, torture and summary killings.

Parliament voted for the Hashdi al-Shaabi to formally become part of Iraq's armed forces in November but the session was boycotted by Sunni representatives who worry it will entrench Shi'ite majority rule as well as Iran's regional influence.

Iraqi and Western officials have expressed serious concerns about the government's ability to bring the Shi'ite militias under greater control.

"International arms suppliers, including the USA, European countries, Russia and Iran, must wake up to the fact that all arms transfers to Iraq carry a real risk of ending up in the hands of militia groups with long histories of human rights violations," said Amnesty researcher Patrick Wilcken in a statement.

States wishing to sell arms to Iraq should ensure strict measures to ensure weapons will not be used by militias to violate human rights, he added.

Amnesty cited nearly 2-1/2 years of its own field research, including interviews with dozens of former detainees, witnesses, survivors, and relatives of those killed, detained or missing.

Its report focused on four powerful groups, most of which receive backing from Iran: the Badr Organisation, Asaib Ahl al-Haq, Kataib Hezbollah and Saraya al-Salam.

Spokesmen for the Hashdi al-Shaabi and for the prime minister, to whom the fighters technically report, did not respond to requests for comment.

A major offensive by Iraqi security forces to retake the northern city of Mosul from Daesh is nearing the end of its third month. Thousands of fighters from various Hashid groups are participating.