Officers from the force said the suspect broadcasted the fatal shooting live on the social network which took place at 635 East 93rd Street, Cleveland, Ohio.
The perpetrator also claimed to have been responsible for several other murders but those claims have not been verified, said spokewoman Sgt. Jennifer Ciaccia.
A statement from Cleveland Police said: “(The) suspect did broadcast the killing on Facebook Live and has claimed to have committed multiple other homicides which are yet to be verified.
“Suspect in this case is a black male Steve Stephens."
The deceased victim from East 93rd Street has been identified as Robert Godwin Sr. age 74.
Cleveland Police Chief Calvin Williams: “Currently there are no other victims that we know of, we have checked multiple areas that are linked to Steve.
“Our officers are currently doubled up and will not be patrolling on their own. Nothing is on lockdown but we ask people to be vigilant.
“We are in touch with Steve’s family members and friends, they are asking him to turn himself in.
“We have checked hundreds of leads and currently there is nothing to connect him to any other incidents. He is considered armed and dangerous.
“We have not had an official sighting of Steve since this incident first happened, from what we can tell it was a random person that he picked out.
"This person obviously needs help and we encourage him to turn himself in, he cannot keep victimising this city.”
Police released this photo of Steve Stephens car
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Police in Cleveland (archive image)
Stephens is believed to be driving a white or cream coloured SUV.
The entire area from East 102 Street to East 108 Street in Cleveland is on lockdown.
Police said Steve Stephens, 37, is described as 6ft1ins and weighing 244lbs.
Stephens is reportedly employed at Beech Brook, a behavioural health agency in northeast Ohio that serves children, teenagers and families, according to a spokeswoman for the facility.
Nancy Kortemeyer, a spokeswoman for Beech Brook, speaking to CNN said: “We are shocked and horrified like everyone else. To think that one of our employees could do this is awful.”
Steve Stephens is being hunted by police in Cleveland
He is bald with a full beard and wearing a dark blue and grey or black striped polo shirt.
Police are investigating claims there are multiple victims with various statements being made on social networking sites about the death toll.
Unconfirmed reports indicate that possibly 15 people have been shot, including an eight-year-old boy.
A man who identified himself as Stevie Steve is seen in a combination of stills on facebook
— Cleveland Police (@CLEpolice) April 16, 2017
Currently, no additional victims have been found, though officers are searching multiple locations, according to police.
The feed has now been taken down from Facebook.
A statement on the force’s website states: ”Cleveland Police are currently investigating a homicide at 635 E. 93. Suspect did broadcast the killing on Facebook Live and has claimed to have committed multiple other homicides which are yet to be verified.
“Suspect in this case is a bm Steve Stephens 6’1 244 bald with a full beard. Wearing dark blue and grey or black striped polo shirt. White or cream colored SUV. Armed and dangerous. If seen call 9-1-1. Do not approach."
On Facebook the suspect wrote that he would not stop killing people until his mum and a woman he names in the video contact him.
It is not known if Stephens has a criminal record or history of violence or mental health issues.
Facebook have responded to the Steve Stephens video and said: “This is a horrific crime and we do not allow this kind of content on Facebook.”
Facebook claims it is “in touch with law enforcement in emergencies when there are direct threats to physical safety”.
Steve Stephens is driving around Cleveland on Facebook Live
An aggravated murder warrant has been issued for Steve Stephens by local authorities.
The Cleveland police division believes the suspect may now be “out of state at this time” and has asked residents in the states of Pennsylvania, New York, Indiana and Michigan to be on alert.
More to follow…