Police in the US state of Ohio have urged residents in surrounding states to be on alert for a man who they said shot and killed an elderly passerby seemingly at random and then posted a video of the murder on Facebook.

Steve Stephens, 37, is wanted on a charge of aggravated murder in the death of Robert Godwin Sr. in the city of Cleveland.

In a statement early on Monday, police warned residents of Pennsylvania, New York, Indiana and Michigan to be on the lookout for Stephens, who they said may have travelled out of state.

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.

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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's 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 in a report by the Associated Press news agency.

"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," said Williams.

Police said Stephens should be considered armed and dangerous. The FBI said it was assisting in the investigation.