Members of the security forces said they had withdrawn from the Anbar Operations Command after it came under attack by the insurgents, who have now trapped them in an area to the west of the city of Ramadi.
One officer among them who asked to remain unnamed said the militants were urging the security forces via loudspeaker to discard their weapons, and promising them safety in return.
The recent Islamic State gains in Anbar province represent the biggest victory for the insurgents in Iraq since security forces and Shi’ite paramilitary groups began pushing them back last year.
A spokesman for Abadi said the prime minister had ordered paramilitaries to prepare to “support the armed forces and restore control over all parts of Anbar”, after the provincial council voted in favor of their deployment.
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.
Earlier on Sunday, the insurgents overran one of the last remaining districts held by government forces in Ramadi, having seized most of the city over the past two days.
A contingent of Iraqi special forces had been holding out in the Malaab neighborhood, but retreated to an area east of the city after suffering heavy casualties, security sources said.
Anbar provincial council member Athal Fahdawi described the situation in Ramadi as “total collapse”.
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.
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.
The 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.
Over a period of 24 hours up to 0500 GMT on Sunday, the U.S.-led coalition carried out seven air strikes near Ramadi, according to a statement — the highest number on any single location in Iraq and Syria.