At present Stephens' claims of other killings can not be substantiated, but the man he shot on social media has been named as 74-year-old Robert Godwin Sr.
Police said early Monday that Godwin is the only victim so far linked to Stephens, despite the suspect's claim in a separate video on Facebook that he killed over a dozen people.
A warning has been issued across five different states over the suspect who filmed himself fatally shooting another man and then shared the video on social media. Police say Stephens broadcast a video on Facebook that showed him get out of his vehicle and shoot a random man walking along East 93rd Street about 2 p.m. Sunday.
Stephens is believed to be driving a recently purchased white Ford Fusion with OH temporary tag E363630, which may have been switched out, Cleveland police chief Calvin Williams said at a news conference Sunday afternoon.
The Facebook Live murder suspect, Steve Stephens, remains at large Monday morning.
The FBI said it was assisting in the investigation.
Authorities also warned people in Pennsylvania, New York, Indiana and MI to be alert for Stephens, who is wanted on a charge of aggravated murder. They're warning residents in the nearby states of Michigan, Indiana, Pennsylvania and NY to be on alert.
"Found me somebody I'm going to kill", he said moments before pulling the trigger. "We don't know why", Williams, the police chief, said.
Just as with extremist content, the uploading of videos such as the murder this weekend highlights the uphill battle Facebook faces.
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Green, a former clerk at the Justice Center Complex in Cleveland who is now on disability, said the conversation confused her.
The company on Sunday called it a "horrific crime", and said that it works hard to "keep a safe environment on Facebook".
Authorities said detectives did initially make contact with Stephens via cellphone after the incident was posted on Facebook, but they were not able to track him or convince him to turn himself in.
Cleveland's police chief says officers have searched dozens of places since the shooting Sunday and told residents to go about their business, but be careful.
Robert Godwin Sr. seen in photo posted online. Stephens Facebook page also has been removed.
A spokeswoman for the agency said they were "shocked and horrified" by what he did Sunday. Stephens allegedly wrote: "I killed 12 people today", and said he wouldn't stop until he could speak to his mother and a second woman.
He approaches the elderly man and demands he repeat the woman's name, "Joy Lane", while pointing the gun at him.
He was driving a white Ford Fusion with temporary license plates, Cleveland police said.
She also said Stephens was "a nice guy" who was generous to everyone and was "kind and loving" to her and her children.