Authorities said that Stephens broadcast the video on Facebook Live around 2 p.m. Sunday (1800 GMT) and that the video was up for around three hours before being taken down.
Police said Sunday night that Stephens "may be out-of-state at this time", and called on residents in Pennsylvania, New York, Indiana and MI to be vigilant.
The FBI is helping with the investigation.
Contrary to earlier reports, a Facebook spokesperson now tells NPR via email that "the murder was not broadcast live on Facebook (it was uploaded), although the suspect did go live at one point during the day".
Cleveland police say they are searching for a homicide suspect who posted a video of the killing on Facebook.
Cleveland police later announced that the deceased victim has been identified as 74-year old Robert Godwin Sr. Some of victims' last moments caught on cameraPolice renewed their urgent plea on Monday for Stephens to turn himself in, and said residents in Pennsylvania, New York, Indiana and MI should be on alert.
In a separate video posted on Facebook, Stephens claimed to have killed 13 other people.
"We are shocked and horrified like everyone else", said Nancy Kortemeyer.
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. "I encourage you to call them and turn yourself in".
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Cleveland residents began tweeting about a man shooting people in the city Sunday afternoon.
"I feel like my heart is going to stop", the grieving woman said.
The shooter - whom police suspect is Steve Stephens, 37 - then asked Godwin's age before killing him.
In January, four people in Chicago were accused of attacking an 18-year-old disabled man while broadcasting the assault on Facebook Live. He was last seen wearing a dark, striped polo shirt. Authorities described Stephens as "armed and risky".
Jackson added that he sent Stephens a text making sure that his friend knew as much.
'This is a horrific crime and we do not allow this kind of content on Facebook, ' said a company spokesperson.
Mr Williams said that the victim appeared to have been selected at random in what he described as a "senseless" murder.
Stephens is a member of the assertive community treatment team at Beech Brook, a mental health organization in northeast OH, a spokesperson for his employer said.
"He is a good guy".
Authorities on Sunday said a series of posts on Stephens' Facebook page complained that he had "lost everything" to gambling, NBC News reported.