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A man who allegedly killed an elderly father after he had enjoyed an Easter meal with his children -- then posted a video of the killing on Facebook -- is the subject of a nationwide manhunt, Cleveland police said Monday.

Steve Stephens, 37, stands charged with Sunday's aggravated murder of 74-year-old Robert Godwin, and police Chief Calvin Williams said law enforcement nationwide are on high alert.

"This is what we would consider a national search for Steve," Williams told reporters. "So, we are not going to leave any stone unturned."

The suspect's mother said that when she last saw Stephens on Saturday, he said it would be a miracle if she ever saw him again. They spoke the next day, she said, and he told her he was shooting people because he was angry with his girlfriend.

Williams said Godwin apparently was chosen at random. "We don't know why."

Appearing alongside a US marshal and an FBI agent, Williams said investigators have searched dozens of locations, "to no avail," and that one of his detectives had spoken to Stephens via cellphone after the killing. He did not elaborate on the call, other than to say the detective attempted to persuade the suspect to surrender.

"We're still asking Steve to turn himself in, but if he doesn't, we'll find him," the chief said. "We're not going to stop until we find him."

He warned any of Stephens' friends or family members who might assist him while he's on the lam: "If you think you're helping Steve, you're really not. You're going to get yourself in trouble."

Report of a cellphone ping

The police chief said authorities didn't know whether Stephens was still in the Cleveland area. There was no evidence Stephens had left Ohio, Williams said.

Earlier, Cleveland police had urged residents in Pennsylvania, New York, Indiana and Michigan to be on alert.

Though Pennsylvania authorities said that Stephens' cellphone had issued a "ping," or a signal, in Erie, Pennsylvania, the Erie Police Department said it had no knowledge of a ping emitted from its city. Erie is about 100 miles east of Cleveland.

Williams told reporters earlier he couldn't speak to the report of a ping. Stephens' last known location was the murder scene, he said.

Stephens is a black male who is 6-foot-1 and weighs 244 pounds. He was last seen wearing a dark blue and gray or black striped polo shirt. He was driving a white Ford Fusion with temporary license plates, Cleveland police said.

"He is considered armed and dangerous, so we want people to be careful out there," Williams told reporters.

Cleveland Mayor Frank Jackson announced a $50,000 reward for information leading to Stephens' arrest.

Horrific footage

The investigation and search for Stephens began Sunday after several people reported an alarming Facebook post, Cleveland police union president Steve Loomis said

Stephens uploaded a video to his Facebook page showing a gun pointed at a man's head.

Seconds before the shooting, Stephens asked the victim to say the name of a woman believed to associated with the suspect.

"She's the reason why this is about to happen to you," Stephens said.

Then, the gunman fires the weapon. The victim recoils and falls to the ground.

The video was posted about 2 p.m. Sunday. Facebook later took it down, calling it prohibited content.

"We work hard to keep a safe environment on Facebook and are in touch with law enforcement in emergencies when there are direct threats to physical safety," a Facebook spokesperson said in a statement.

Stephens claimed on Facebook that he committed multiple homicides, but police said they had no knowledge of other victims. He has many traffic violations but no criminal record, Williams said.

"Obviously, he's got deep, deep issues," the chief said.

As Cleveland police and the FBI were searching for Stephens, more than 300 tips poured into the department, police said.

No confirmed sightings of Stephens were reported as the search moved into Monday.

'If you see me again, it'll be a miracle'

Stephens' mother, Maggie Green, said the oldest of her three children came by her house Saturday afternoon.

"He said this (was) the last time I was going to see him," recalled Green, 53.

Green, a former clerk at the Justice Center Complex in Cleveland who is now on disability, said the conversation confused her.

"If you see me again, it'll be a miracle," she quoted him as saying.

Green learned about the shooting when her youngest son told her about the video.

She was "just dumbfounded" and called Stephens. He told her he was "shooting people" because he was "mad with his girlfriend" of about three years, she said, explaining it was a brief phone call because her phone died.

The woman believed to be associated with the suspect has told multiple news agencies that she was "overwhelmed" by the tragedy.

"Steve really is a nice guy... He is generous with everyone he knows. He was kind and loving to me and my children," she told CBS News.

Williams said police have spoken to her, and she is safe and cooperating with the investigation. The woman's neighbors told CNN that Stephens often stayed at her Twinsburg home with her three young girls. One resident said Stephens was there two days ago fixing the home's garage.

'We are shocked'

Police have not talked about a possible motive in the shooting. Stephens and Godwin didn't know each other, authorities said.

Stephens is employed at Beech Brook, a behavioral health agency in northeastern Ohio that serves children, teenagers and families, according to a spokeswoman for the facility.

"We are shocked and horrified like everyone else," said Nancy Kortemeyer. "To think that one of our employees could do this is awful."

Kortemeyer could not provide Stephens' job title, nor could she say how long he'd worked at Beech Brook. Stephens' mother said he was a social worker.

Beech Brook was closed Monday "for the safety of our employees," Kortemeyer said. "At this point, we'll just be closing today, but we'll take it day by day."

Victim was 'a good man'

Robert Godwin was walking on the sidewalk when he met Stephens.

He was on his way home from an Easter meal at his children's home when he was killed, CNN affiliate WOIO reported.

Brenda Haymon, Godwin's youngest child from his first marriage, said he was a father of 10.

"He lived a good life. He's a man people should model themselves after," she said.

One of his sons, Robert Godwin Jr., told WOIO that his father's death isn't real to him yet.

"He is a good guy. ... He'd give you the shirt off his back, and I'm not just saying that for these cameras," he told the station. "This man right here was a good man. I hate he's gone ... I don't know what I'm going to do."

Williams told reporters that the victim's family has reported several bogus GoFundMe accounts and asked that people refrain from contributing to any of them until the Godwins send out official details.

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