The two fighters "succumbed after having been wounded while they were confronting an attack" by jihadists late Saturday in Salaheddin province north of Baghdad, the Hashed said in a statement carried by Iraqi state media.

A security source, speaking to AFP on condition of anonymity, confirmed the death toll and said that IS attacked a Hashed "(military) post on Saturday night" in the area of Al-Zarka in the province's north.

Hashed al-Shaabi is a coalition of mainly pro-Iranian former paramilitary units that have been integrated into the regular armed forces.

Iraqi troops have been heavily involved in the fight against IS, also opposed by Tehran.

IS claimed the attack in a statement published on the group's Telegram channels, saying two Hashed members had been killed and three others wounded.

Hours after the attack, the Iraqi military bombarded IS "hideouts" in Diyala province near Salaheddin, killing five of the group's fighters, according to the government's media unit for security affairs.

IS jihadists seized swathes of Iraq and neighbouring Syria in 2014, declaring a "caliphate" which they ruled with brutality before their defeat in late 2017 by Iraqi forces backed by a US-led military coalition.

Jihadist cells, however, still stage sporadic attacks on the army and police, especially in rural and remote areas.

A United Nations report published in July said IS has "between 5,000 and 7,000 members across Iraq and the Syrian Arab Republic, most of whom are fighters".