Law enforcement officials identified the suspect as 37-year-old Steve Stephens, and Cleveland police said officers were searching for him.
A cell phone belonging to Stephens was pinged overnight on the east side of Erie County, Pennsylvania, according to City of Erie Police Sgt. Robert Hill, but there have been no legitimate sightings of the suspect.
DISTURBING VIDEO WARNING: Some of victims' last moments caught on camera
Police renewed their urgent plea on Monday for Stephens to turn himself in, and said residents in Pennsylvania, New York, Indiana and Michigan should be on alert. He is considered armed and dangerous.
Cleveland Police Chief Frank Jackson revealed detectives initially made contact with Stephens via cellphone after the video of the murder was posted, but were unable to track him or convince him to turn himself in.
The U.S. Marshall's Office said local and federal resources were being used to find Stephens.
"Quite frankly, at this point he could be in a lot of places," Cleveland FBI agent Steve Anthony said. "He could be nearby, far away, or anywhere in between."
On Sunday, police identified Stephens' victim as 74-year-old Robert Godwin Sr.
In a statement, Facebook said the suspect did go live on the social media site at one point during the day, but not during the killing. Police earlier Sunday had said that Stephens had broadcast it on Facebook Live.
In the video, which appears shaky, Stephens gets out of his car and appears to randomly target Godwin, who was holding a shopping bag. Stephens says the name of a woman, whom Godwin does not seem to recognize.
"She's the reason that this is about to happen to you," Stephens told Godwin before pointing a gun at him. Godwin can be seen shielding his face with the shopping bag.
Cleveland Mayor Frank Jackson publicly urged Stephens to turn himself into police and not to "do any more harm to anybody."
"Any problems he is having, we can have a conversation," Jackson said.
In a separate video, Stephens claimed to have killed more than a dozen other people. Williams said police have not verified any other shootings or deaths.
"There are no more victims that we know are tied to him," he said.
The chief also said they've been talking with family and friends of Stephens, who is employed at Beech Brook, a behavioral health agency headquartered in Pepper Pike, near Cleveland.
"We are shocked and horrified and we don't know anything more about it," agency spokeswoman Nancy Kortemeyer told WOIO-TV. "We hope and pray that he is arrested as soon as possible and we hope and pray for a resolution quickly."
It was not immediately known what Stephens does for the agency, which said it will serve more than 18,000 children and families this year, according to its website.
Joy Lane, who previously dated Stephens for several years, released a statement saying in part that Sunday's turn of events are difficult to deal with.
"My heart and prayers goes out to the family members of the victim(s), Steve really is a nice guy...he is generous with everyone he knows," Lane said. "He was kind and loving to me and my children."
The video of the killing was up on Facebook for about three hours before it was removed. Stephens' Facebook page also has been removed.
"This is a horrific crime and we do not allow this kind of content on Facebook," said a spokesperson for Facebook. "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."
Police said Stephens should be considered armed and dangerous. Late Sunday, police issued an aggravated murder warrant for him and in a statement said that he may have traveled out of state.
The FBI is assisting in the investigation.
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