Steve Stephens, 37, is wanted on a charge of aggravated murder in the death of Robert Godwin Sr. in Cleveland.
In a statement early on Monday, police warned residents of Pennsylvania, New York, Indiana and Michigan to be on the lookout for Stephens.
In the video, which appears shaky, Stephens gets out of his car and appears to randomly target Godwin, 74, who is holding a plastic shopping bag. Stephens says the name of a woman, whom Godwin does not seem to recognise.
“She’s the reason that this is about to happen to you,” Stephens tells Godwin before pointing a gun at him. Godwin can be seen shielding his face with the shopping bag.
Facebook said the suspect did go live on the social media website at one point during the day, but not during the killing. Police earlier had said that Stephens had broadcast it on Facebook Live.
The video of the killing was on Facebook for about three hours before it was removed. Stephens Facebook page also was eventually removed.
“This is a horrific crime and we do not allow this kind of content on Facebook,” said a company spokesperson. “We work hard to keep a safe environment on Facebook, and are in touch with law enforcement in emergencies when there are direct threats to physical safety.”
The victim’s son, Robert Godwin Jr., told Cleveland.com that he can’t bring himself to watch the video.
“I haven’t watched the video. I haven’t even looked at my cellphone or the news,” Godwin said. “I don’t really want to see it.”
He said his father, a retired foundry worker, collected aluminum cans and often walked with a plastic shopping bag, picking cans up if he saw them on ground. The son said he believed his father was looking for cans on Sunday when Stephens approached him.
In a separate video posted on Facebook, Stephens claimed to have killed more than a dozen other people.
“Like I said, I killed 13, so I’m working on 14 as we speak,” he said.
Police have not verified any other shootings or deaths, Police Chief Calvin Williams said.
“There are no more victims that we know are tied to him,” he said.
Police said they have been talking with family and friends of Stephens, who is a case manager at Beech Brook, a behavioral health agency headquartered in Pepper Pike, near Cleveland.
“We were shocked and horrified to learn of this news today,” agency spokeswoman Nancy Kortemeyer said in a statement. “We are hoping that the Cleveland Police will be able to apprehend Mr. Stephens as soon as possible and before anyone else is injured.”
In one of the videos, Stephens can be seen holding up his Beech Brook employee identification badge.
“I’m killing with my Beech Brook badge on too,” he says.
Stephens also mentioned his fraternity, Omega Psi Phi, in one of his Facebook posts. The fraternity issued a statement Sunday night.
“On behalf of the Supreme Council and the members of Omega Psi Phi Fraternity, Incorporated, we lift our sincere and heartfelt prayers and condolences of comfort to the families impacted by the recent shooting in Cleveland, Ohio,” it said.
Police said Stephens should be considered armed and dangerous.
The FBI said it was assisting in the investigation.