BAGHDAD: Iraqi forces said Friday that Daesh fighters are withdrawing deep into the desert to escape an offensive aimed at a final defeat of the militants.

Daesh has already been driven out of all of the towns it once held, but Prime Minister Haider al-Abadi has said he will not proclaim victory until the militants have been cleared from the western desert bordering Syria.

The Hashed al-Shaabi (Popular Mobilisation) paramilitary force said its fighters had taken control of 77 villages and hamlets since the launch of the offensive on Thursday morning.

It said five militants had been killed south of the ancient desert city of Hatra, but otherwise Daesh had put up little resistance.

The Hashed said that its fighters overran an airfield in the same area, where they discovered underground warehouses used by the militants.

Air support for the offensive, which also involves the army and federal police, has so far been provided exclusively by the Iraqi air force.

The US-led coalition, which has provided air support for other offensives against Daesh in Iraq, said it carried out no strikes on Thursday.

"We will provide strikes if we know that there is an ISIS (IS) cell, or tunnels, or something there," coalition spokesman US Colonel Ryan Dillon told AFP.

"If the requests are not coming, we won't do a strike... it's supply and demand," he said.

"And when you're in such a vast wide open desert area... there's less of a requirement for precision-guided missiles," unlike in urban areas.

At its peak in 2014, Daesh ruled over seven million people in a territory as large as Italy encompassing large parts of Syria and nearly a third of Iraq.

It is now being flushed out of its last desert hideouts in Iraq and under attack by Russian-backed government forces and US-backed Kurdish-led fighters in its last pockets of control in Syria.