"She’s the reason that this is about to happen to you,” the shooter says in the video, according to multiple reports. A handgun then fires and Godwin is shot in the head.
Cleveland Police Chief Calvin Williams said Monday that a $50,000 reward is being offered for information leading to Stephens' arrest.
The last ping from the man's cell phone was reported near Philadelphia, he said. He warned the public to remain vigilant and watchful.
"He is, without a doubt, armed," the chief said at a press conference.
Cops say the shooter, who fled the scene after firing the fatal shot, purports to have killed more than a dozen others in what he called an "Easter Day slaughter."
But Williams, said, "There are no other victims that we know of."
Video of the shooting was uploaded to Facebook at about 2 p.m., not broadcast live as was originally reported, according to a Facebook spokesperson.
Homes belonging to the suspect and his relatives had been searched Monday and additional weapons were found, he said. The murder weapon was a handgun that is still believed to be in Stephen's possession, he said.
Cleveland Mayor Frank G. Jackson also addressed the tragedy.
"Steve Stephens killed an elderly gentleman; I personally give my condolences to the family of the victim," Jackson said. "We know who Steve Stephens is and he will be eventually caught. He need not to do anymore harm to any innocent people. Whatever concerns or problems that he’s having, we’re here to have a conversation."
Stephens is described as a 6-foot-1 inch man weighing 244 pounds with a bald head and a full beard. He was last seen wearing a dark blue and grey or black striped polo shirt. Authorities say he was driving a four-door white Ford Fusion with a temporary tag.
The chief also touched on the woman who they say Stephens named in the video. That woman, Williams said, is safe, but he did not disclose her location.
That woman, Joy Lane, offered her condolences to the family of the victim in a text message to CBS News.
“We had been in a relationship for several years," she wrote. "I am sorry that all of this has happened. My heart & prayers goes out to the family members of the victim(s).
"Steve really is a nice guy... he is generous with everyone he knows. He was kind and loving to me and my children. This is a very difficult time for me and my family. Please respect our privacy at this time."
At least one person identifying himself as a family member of the victim also asked for privacy as video of Godwin's shooting continued to spread across social media, even after Facebook took it down.
Godwin was reportedly a grandfather of 14.
"Please please please stop retweeting that video and report anyone who has posted it!" Ryan Godwin tweeted Sunday. "That is my grandfather show some respect
#Cleveland. If you guys are going to exploit my grandfather's legacy for some retweets at least honor him by getting his name right GOD-WIN not Goodwin."