Iraqi Prime Minister Haider al-Abadi on Sunday ordered government forces to "hold their positions" in Ramadi, after the Islamic State group said it overran the strategic city, his spokesman said.

Abadi said troops, tribesmen and other elite forces "must hold their positions and preserve them and not allow Daesh (IS) to extend to other areas in Ramadi," spokesman Saad al-Hadithi said.

"There is continuous air cover that will help ground troops there hold their positions while waiting for support from other forces and the Popular Mobilisation Units," he said of an umbrella group for Shiite militias.