A trapped militant "detonated his explosives belt, killing a major and another soldier, also wounding three others", an interior ministry source told AFP, asking not to be named.

A second Islamist militant was killed when he also tried to set off a suicide bomb in the army operation in the rural area of Tarmiya, the source said.

IS overran large swathes of Iraq and neighbouring Syria in 2014, declaring a "caliphate", before Baghdad declared victory in late 2017 after a grinding campaign.

But a low-level jihadist insurgency has persisted, particularly in rural areas north of Baghdad around the city of Kirkuk and in the eastern provinces of Diyala and Salaheddin.

On Tuesday, Iraqi military command spokesman Yahya Rassoul said "43 Islamic State elements" had been killed in a recent operation in the northern province of Niniveh, of which the former IS bastion Mosul is the capital.

According to a UN report last year, some 10,000 IS fighters remain active in Iraq and Syria.