The Iraqi city of Ramadi has been captured by Islamic State after days of intense fighting and bombings by the terror group, officials say.

"Ramadi has fallen," said Muhannad Haimour, spokesman for the governor of Anbar province. "The city was completely taken ... It was a gradual deterioration. The military is fleeing."

He also confirmed the provincial command centre in the city had fallen into enemy hands.

A colonel among troops who had withdrawn added: "Daesh has just taken full control of all main security bases", using an Arabic acronym for IS.

But Iraqi Prime Minister Haider al-Abadi ordered government forces to "hold their positions". He called on troops, tribesmen and other elite forces to push the militants out of Ramadi.

The United States said it was monitoring the fighting in the city and described the situation as "fluid and contested".

"It is too early to make definitive statements about the situation on the ground there at this time," Pentagon spokeswoman Maureen Schumann said.

An estimated 500 people - militants and civilians - have been killed in Ramadi over the last two days and around 8,000 have fled as IS launched a fierce offensive of suicide car bomb attacks.

Fifteen Iraqi troops and police died on Sunday in four near-simultaneous car bombings, with soldiers retreating and leaving behind vehicles and weapons.

A purported message by Islamic State on a jihadist internet forum also appeared to confirm the city was firmly in its grip.

"God has enabled the soldiers of the caliphate to cleanse all of Ramadi," read the message.

One officer inside the captured command base described being surrounded, with mortars "raining down" and IS fighters "in almost every street".

Local television also reported that Iraq's prime minister, Haider al Abadi, is sending in Shia militias and has urged troops to hold their positions until they arrive.

The militias have played a key role in fighting IS in other areas of Iraq but there are worries they could stir up sectarian violence in Sunni-dominated Anbar.

Islamic State's fresh offensive seized most of Ramadi on Friday, with their black flag raised over a local government headquarters.

Ramadi, a city of around half a million and just 110km (70 miles) from Baghdad, is one of a few places in the sprawling desert terrain of Anbar province that had managed to hold out against IS.

Fighting has been raging there since last year, but IS renewed their push for the city in April.