Islamic State militants overran one of the last remaining districts held by government forces in the Iraqi city of Ramadi on Sunday and besieged a key army base on the edge of the western provincial capital, security sources said.

The militants seized most of Ramadi on Friday, planting their black flag on the local government headquarters in the centre of the city, but a contingent of Iraqi special forces was holding out in the Malaab neighborhood.

Those forces retreated on Sunday to an area east of the city after suffering heavy casualties, security sources said, bringing Ramadi to the brink of falling to Islamic State.

It would be the first major urban centre to be seized by the insurgents in Iraq since security forces and paramilitary groups began pushing them back last year.

Anbar provincial council member Athal Fahdawi described the situation in Ramadi as "total collapse" and said local officials had voted in favour of the deployment of Shi'ite paramilitaries to the Sunni heartland.

Shi'ite paramilitaries have played a leading role in reversing Islamic State gains elsewhere in Iraq, but have so far been kept on the sidelines in Anbar due to concerns about inflaming sectarian violence.

The insurgents were closing in on the Anbar Operations Command to the west and a military officer inside the army base said it was too late to send reinforcements, pleading for help from Iraqi Prime Minister Haider al-Abadi.

"We are now surrounded inside the Operations Command by Daesh, and mortars are raining down," said the officer. Daesh is an Arabic acronym for Islamic State.

"Daesh fighters are in almost every street. It's a chaotic situation and things are sliding out of control. Ramadi is falling into the hands of Daesh," the officer said.

Islamic State, which emerged as an offshoot of Al Qaeda, controls large parts of Iraq and Syria in a self-proclaimed caliphate where it has massacred members of religious minorities and slaughtered Western and Arab hostages.

United States and its allies have been pounding the militants for months with air strikes in both countries. Washington said on Saturday its special forces had killed a senior IS figure in a raid into Syria.

Ramadi is the capital of Anbar, Iraq's largest province, and one of just a few towns and cities to have remained under government control in the vast desert terrain, which borders Saudi Arabia, Syria and Jordan.  - Reuters