A nationwide manhunt is under way in the US for the suspect who shot dead a grandfather on the street apparently at random and posted the footage.
The suspect, Steve Stephens, said in another video post that he had killed 13 people and would kill more.
He shot dead 74-year-old Robert Godwin in Ohio as the victim walked home from Easter lunch on Sunday afternoon.
Facebook has launched a review of its procedures after criticism that the footage stayed on the site for hours.
Justin Osofsky, Facebook’s vice-president of global operations, said the first complaint made about the video showing the killing came nearly two hours after it was posted.
But he added: “We know we need to do better.”
Police have asked residents of Ohio, Indiana, Michigan, New York and Pennsylvania to be on the alert, saying suspect could be anywhere.
Cleveland police department have issued a photo of Mr Stephens, 37, on its website, describing him as a black male, 6ft 1in (1.86m) and 244lb (110kg).
Cleveland Police Chief Calvin Williams told reporters on Monday that Mr Stephens, who has a licence to carry a concealed firearm, is armed “without a doubt”.
Cleveland officials have also offered a $50,000 (£39,805) reward for information that leads to his location.
His mobile phone signal was last tracked on Sunday afternoon in Erie, Pennsylvania.
Cleveland Police Chief Calvin Williams said in a press conference on Monday morning: “Steve is still out there some place… we’re still asking Steve to turn himself in, but if he doesn’t we’ll find him.”
FBI Special Agent Stephen Anthony said: “Quite frankly, he could be in a lot of places.”
US Marshall Peter Elliot said law enforcement agencies across the US were helping create a dragnet to “make this individual’s world very, very, very small”.
Investigators said Mr Stephens’ boast about other killings was still not verified.
Police say the victim in Sunday’s graphic video appeared to have been selected at random.
The suspect approaches Mr Godwin and asks him to say the name of a woman believed to be the gunman’s former girlfriend, before shooting him in the head.
“Can you do me a favour?” asks the gunman. “Can you say Joy Lane?”
The victim says: “Joy Lane.”
Mr Stephen says: “Yeah, she’s the reason why all this about to happen to you. How old are you?”
The grandfather and father of nine appears to try to shield himself by holding up a plastic bag.
The woman, Joy Lane, confirmed to CBS News that she and Mr Stephen had been in a “relationship for several years”.
“I am sorry that all of this has happened. My heart & prayers goes out to the family members of the victim(s). Steve really is a nice guy… he is generous with everyone he knows.
“He was kind and loving to me and my children,” she wrote in a text message.
Maggie Green, the suspect’s mother, told CNN that he was “mad with his girlfriend. That’s why he is shooting people and he won’t stop until his mother or girlfriend tell him to stop.”
Mr Stephens is employed by Beech Brook, a children’s behavioural health agency, according to a company spokesman.
Facebook murder suspect Steve Stephens hunted across US