Police Chief Calvin Williams said during a press briefing Monday that police have searched "dozens" of locations in response to leads but haven't found Stephens yet. Until Facebook facilitates a foolproof system of supervising streams, then the Facebook Live platform remains vulnerable to undetected broadcasts of violence, sex, and other types of content that go against the site's policy.
The video of the killing was posted on Facebook for about three hours before it was removed.
In the video showing the shooting of Godwin, a man resembling Stephens exits his auto, saying, "I found somebody I'm about to kill".
In a separate video posted on Facebook, Stephens claimed to have killed more than a dozen other people. In a statement, they said he may have traveled out of state.
"There is no need for any further bloodshed in this incident tonight", Williams said at a news conference, adding that "We need to bring this to a conclusion today" and "We need to get Steve from the streets".
The new video is reigniting old questions about how the social network handles offensive content: How many people does Facebook have moderating and flagging this type of content globally?
The search has spread to four neighbouring states: Pennsylvania, New York, Indiana and MI.
Mr Williams said the shooter, Steve Stephens, 37, is armed "without a doubt".
He also posted several times in the hours before the shooting, calling his upcoming behaviour an "Easter day slaughter".
Stephens asked the victim to say the name of a woman believed to be associated with the suspect.
Stephens is wanted for the Easter killing of 74-year-old Robert Godwin, Sr.
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In one of the videos, Stephens could be seen holding up his employee identification and said: "I'm killing with my Beech Brook badge on, too".
Williams said authorities have yet to determine a motive for the shooting.
Authorities searched Sunday night across the Cleveland area for the suspect, who they said is African-American, 6-foot-1, bald and has a full beard.
"I don't think they understand that the correct answer is zero", says Brian Wieser, an analyst who covers both companies at Pivotal Research Group.
"That man killed my daddy for no reason", said 8-year-old Marsean Robert Godwin, named for his dad. "I am sorry that all of this has happened".
The FBI has now joined in the hunt, offering a $50,000 reward for any information leading to Stephens' arrest.
"He is considered armed and risky, so we want people to be careful out there", Williams told reporters. "Should Facebook have a duty to rescue a crime victim?"
Authorities received more than 400 tips from the public related to Stephens.
In the case of the most recent murder video, almost two hours passed before users reported it on Facebook, according to the company.
Detectives spoke with Stephens on Sunday by cellphone and tried to persuade him to surrender, police said.