Fighters from ISIL have killed at least 10 Iraqi soldiers in the country's western province of Anbar, according to officials.

No claim of responsibility for the killing has been made.

"We had 10 soldiers killed and six wounded in an attack by Daesh early this morning," an army lieutenant-colonel told AFP news agency on Tuesday, using the Arabic acronym for ISIL, or the Islamic State of Iraq and the Levant group, also known as ISIS.

Speaking to AFP, a police officer and a local official confirmed the attack and casualty toll.

In a separate incident earlier on Tuesday, armed men fatally shot a senior executive of Iraq's state-run North Gas Company (NGC) as he was heading to his office in the northern oil city of Kirkuk, police and company sources said.

Mohammed Younis, Iraqi Kurdish deputy manager of NGC, and his driver were killed instantly when assailants in a speeding car fired on their vehicle, police sources said.

Kirkuk has a mixed population of Kurds, Turkmens and Arabs.

It has been under Kurdish control since June 2014, when ISIL overran the northwest of the country and Iraqi security forces collapsed.

The largest city in northern Iraq, Mosul was captured by ISIL in mid-2014.

On April 23, ISIL fighters attacked a police base in a town that is being used as a staging ground for the Mosul offensive, killing at least three policemen.

Backed by the US-led coalition, Iraqi forces launched an operation, their largest in years, in mid-October last year to retake the city.

They retook the side of the city that lies east of the River Tigris in January and launched a push on remaining ISIL fighters in western Mosul, which is more densely populated and has seen fierce fighting.

On the west bank of the Tigris, Iraqi forces control southern neighbourhoods and are slowly surrounding Mosul's Old City, whose narrow streets are expected to make federal operations very difficult.

Residents who managed to escape from the Old City say that there is almost nothing to eat but flour mixed with water and boiled wheat grain.

The loss of Mosul would be a huge blow to ISIL.

OPINION: Iraqi Kurdistan - Playing the independence game

According to an Iraqi military spokesman, ISIL only controls 7 percent of Iraq, down from the 40 percent of the national territory over which it ruled three years ago.

The only two other significant towns ISIL still holds are Hawija and Tal Afar. The group also controls territory in remote areas of western Iraq, near the Syrian border.

Iraqi forces on Thursday launched a fresh push against ISIL-held villages there, as part of a months-old operation to retake areas along the Euphrates in Anbar.

Fighting has killed several thousand civilians and fighters on both sides, according to aid organisations.