Police initially reported that Stephens broadcast the murder on Facebook Live.
Stephens uploaded a video to his Facebook page showing a gun pointed at an unidentified man's head.
In the video, Stephens said he snapped because of a woman, and then later claimed to have killed more than a dozen other people.
The woman Stephens mentioned is one person police have spoken to in the investigation, Williams said.
A manhunt that started in Cleveland's gritty east side expanded rapidly into a nationwide search for Stephens, a 37-year-old job counselor who worked with teens and young adults, police said.
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. People have been asked to remain vigilant in Pennsylvania, New York, Indiana, and MI.
"We just hope Mr. Stephens is apprehended as quickly as possible so that no one else is injured", she said.
"He could be a lot of places", said Stephen Anthony, the FBI's top agent in Cleveland. They said Stephens and Godwin didn't know each other.
The minute-long video was up for several hours on "Stevie Steve's" Facebook account and viewed thousands of times before it was removed.
The man also claimed to have committed multiple other homicides.
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"We are shocked and horrified and we don't know anything more about it", agency spokeswoman Nancy Kortemeyer told CBS Cleveland affiliate WOIO-TV. They've described him as being a bald, black man with a full beard, standing 6 foot 1 inch and weighing 240 pounds. We'll move quickly to correct the record and we'll only point to the best information we have at the time.
Mr Williams said that authorities had put out alerts "in the state of OH and beyond" over the "senseless" incident, and urged people not to approach the suspect, who he said was likely to remain armed and risky.
The victim was identified as 74-year-old Robert Goodwin Sr.
Police say the suspect's vehicle is a white Ford Fusion with temporary tag E363630.
The shooting is the latest violent incident shown on Facebook, raising questions about how the world's biggest social media network moderates content.
"Any problems he is having, we can have a conversation", Jackson said. He'd give you the shirt off his back and I'm not just saying that for these cameras...
"We've searched high and low throughout this city", Williams told reporters.
"Hopefully I'm gonna try to kill as many people as I can".
"He needs to turn himself in so that he can get the help that he needs and he can't keep victimizing this community based on his issues", Williams said.