The men belonged to the Noujaba Movement, a part of the Hashed al-Shaabi coalition of Shiite militias that mostly back Iran.

Both sources said they were killed in an attack by IS on their base in Tarmiya, north of Baghdad, with seven more fighters wounded.

Formed in 2014 to back the Iraqi army in its fight against IS jihadists, the Hashed at the time controlled large swathes of the country but have since been integrated into the armed forces.

In recent months the anti-American movement has hailed attacks on American interests in Iraq, without claiming responsibility.

Both the US and Israel fear some Hashed units are under Iranian orders rather than the Iraqi chain of command.

Some IS jihadist cells have remained active even after Iraq declared the jihadist group defeated in 2017, especially in the Tarmiya region and the deserts of northern Iraq.

They have attacked Iraqi security forces as well as the Hashed and other Shiites, who form the majority of Iraq's Muslims but are seen by IS as apostates.

Last month, IS claimed responsibility for an attack that killed 30 people at a market in the densely-populated Sadr City area of Baghdad.