The two fighters "succumbed after having been wounded while they were confronting an attack" by IS in Salaheddin province north of Baghdad, the Hashed said in a statement reported by the official INA news agency.

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

The Hashed al-Shaabi is a coalition of mainly pro-Iranian former paramilitary units, mostly from the Shiite branch of Islam, now integrated into the Iraqi armed forces, whose fighters have been heavily involved in the fight against IS.

Hours after the attack, the government's media unit for security affairs said the army had bombarded IS "hideouts" in adjacent Diyala province, killing five IS fighters.

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.

However, jihadist cells 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".