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Oklahoma police are hunting a double murder suspect who authorities say live-streamed his getaway after a shoot-out with officers.

Michael Vance, 38, posted two Facebook videos after wounding two police officers on Sunday night.

He allegedly escaped in a patrol car and killed two relatives, nearly decapitating one of them.

Vance indicated he intended to target several people linked to a sexual assault case against him.

"Letting y'all know, look, this is real," the suspect, wearing a blood-soaked shirt, said in one of the videos, which police believe was filmed inside the stolen police car.

"If you want to know what's up next, stay tuned to your local news," said Vance.

He added that things are "going to get intense".

In one of the videos he showed off what he said was an AK-47 rifle in the front seat of a car.

The bloodshed began on Sunday night after two police officers responded to a report of shots fired in Wellston, 35 miles (56km) northeast of Oklahoma City.

Both officers were wounded during a subsequent gun battle with Vance, authorities said.

Wellston Officer Jim Hampton, who was shot in the foot, told Oklahoma City television station KOCO he shot the suspect twice.

"He fell to the ground again, laid there for a few minutes, got back up. The firefight was on again.

"At one time, we was actually standing up facing each other, shooting at each other."

Lincoln County Sheriff's Office said Vance fled in a police car.

The construction worker is suspected of later shooting a woman and stealing her 2007 Mitsubishi Eclipse at a mobile home park near Wellston.

He then allegedly drove about eight miles (12km) to the mobile home of two relatives and killed them.

In an affidavit, police say Vance attempted to decapitate Robert Everett Wilkson, 55, and cut off the arm of Valeri Kay Wilkson, 54, in a "rage killing".

Vance is also suspected of shooting a man in the leg in an attempted carjacking early on Monday at a convenience store in Sayre, about 30 miles from the Texas border.

He was recently released from Lincoln County Jail in Oklahoma, where he was being held on an allegation of sexually assaulting a 15-year-old girl.

Vance, who has a Grim Reaper tattoo on one arm, according to the Oklahoman newspaper, had been scheduled to appear in court next month to face the felony charges.

There have been no sightings of him since Monday and Oklahoma County Sheriff John Whetsel said he "could be anywhere from California to Mexico to Florida".

Vance is now also facing two counts of murder, one count of unauthorised use of a motor vehicle and possession of a firearm after conviction of a felony, according to court documents.

Police said Vance has a communicable disease that he "may attempt to spread".

The Oklahoma County Sheriff's office did not release his medical condition.

But officials told ABC News: "We would urge caution to anyone who comes in contact with this individual."

Vance has previously been convicted of a 2001 felony bogus cheque charge, a 2009 misdemeanor marijuana offence and a 1999 misdemeanor assault charge.