The police chief said: "We are not going to pinpoint a specific thing and say this is what triggered this because we don't know".
Stephens then posted a video of the crime to Facebook.
Stephens, 37, allegedly shot dead 74-year-old Robert Godwin as the victim walked home from Easter lunch on Sunday afternoon in Cleveland.
It wasn't immediately clear where Stephens had been since Sunday. They have asked anyone who spots him or his vehicle to contact police or the Federal Bureau of Investigation.
Police say Steve Stephens was spotted on Tuesday morning by state officers in Erie County, in the state's north-west corner.
Smalls said if Steve Stephens, the man who is accused of murdering Godwin, is watching, she would want him to hear her son, "My daddy didn't do anything to anyone he just shot him for no reason, for no reason". A warrant was issued for his arrest on a charge of aggravated murder.
He posted a video of that shooting on Facebook. A $50,000 reward is being offered for information leading to his capture and prosecution.
Cleveland police chief Calvin Williams confirmed one killing but said they did not know of any other victims.
"We are shocked and horrified like everyone else", Nancy Kortemeyer, a spokeswoman for the facility told the local news network. She said Stephens was "a nice guy" who was generous to everyone. But he says these searches can take days, weeks or even longer.
In the video, Stephens blamed a former girlfriend he had lived with, saying he woke up last week and "couldn't take it anymore". He has many traffic violations but no criminal record, Williams said.
The video appeared to show the gunman asking Godwin to say Stephens' girlfriend's name before shooting him in the head.
Authorities say Stephens is considered armed and risky and could be anywhere.
The company on Monday said it would begin reviewing how it monitors violent footage and other objectionable material in response to the killing.
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.
A second video circulated on social media showed him talking to someone, and claimed that he had "snapped" and that he killed 13 people, and that he will keep killing "until they catch" him.
In a statement on Monday, Facebook said it will review its content reporting system to make it easier for users to flag content that may violate its rules.