The man who allegedly killed a stranger in a video uploaded to Facebook told his mother before the shooting that, "If you see me again, it'll be a miracle".
Maggie Green, the mother of accused murderer Steve Stephens, told CNN that he visited her Saturday afternoon, before the shocking act of violence. Later, Mr Stephens told her on the phone that he was "shooting people" because he was "mad with his girlfriend".
Authorities admit that they don't know the whereabouts of the 37-year-old, who disappeared after shooting Robert Godwin Sr, 74, in the head in Cleveland, Ohio, on Sunday, news.com.au reported.
Five American states are on high alert as police, the Federal Bureau of Investigation and the US Marshals Service hunt for the children's mental health worker, who apparently chose to kill Mr Godwin at random.
Cleveland mayor Frank Jackson announced on Monday afternoon that a $US50,000 reward was on offer for information that leads to Mr Stephens' arrest.
Mr Stephens' mobile phone last released a signal, or ping, in Erie, Pennsylvania, 165km northeast of Cleveland, authorities told CNN, but Cleveland police chief Calvin Williams said his last confirmed location was the scene of the crime.
While the suspect's mother pointed to his relationship with his ex-girlfriend as a motive for the shooting, Mr Williams said there was no "rhyme or reason for it happening".
"We, at this point, cannot concentrate on one issue that may or may not have led to this," he said.
Mr Williams said detectives spoke with Mr Stephens via mobile phone after the "heinous crime" but he had since slipped through the authorities' grasp.
"They tried to convince him to turn himself in and of course that hasn't happened to date," Mr Williams told reporters at a press conference on Monday.
Mr Stephens turned to violence because he was angry with his ex-girlfriend Joy Lane, he says in a video posted to Facebook.
She told CBS News in a text message that she was "sorry that all of this has happened".
"My heart & prayers goes out to the family members of the victim(s)," she wrote.
"Steve really is a nice guy ... he is generous with everyone he knows. He was kind and loving to me and my children."
In the video, which has since been taken down from the social media site, Mr Stephens approaches Mr Godwin and asks him to repeat Joy Lane's name saying, "She's the reason this is about to happen to you".
He pulls the trigger on the gun and the man falls to the ground, with blood rushing from his face.
Mr Stephens wrote on Facebook he wouldn't stop killing until he received a call from his mother and Ms Lane.
Mr Williams said officers had searched for the suspect at dozens of locations "to no avail".
Mr Stephens said in Facebook comments that he had killed 15 people in Cleveland, but Mr Williams said there was no evidence that he had killed anyone other than Mr Godwin.
The police chief warned residents that there was a lot of misinformation doing the rounds on social media.
"We don't want people to panic," Mr Williams said.
"Unfortunately, there's been one fatality, one homicide in this entire scenario, and we want to keep it that way.
"We're still asking Steve to turn himself in, but if he doesn't we'll find him ... we're not going to stop until he's in custody."
Mr Williams said the suspect had no criminal history but "obviously, he's got deep, deep issues".
FBI special agent in charge of the investigation, Stephen Anthony, said the goal was to find Mr Stephens before there was any further violence.
"This individual is armed and dangerous and, quite frankly, at this point he could be a lot of places. He could be nearby, he could be far away and anywhere in between," he said.
"We need to take this individual off the street ... rest assured that we're using any and all resources to work this, not just in the Cleveland area, but throughout the United States."
US Marshall Peter Elliott said he was "optimistic" Mr Stephens would be found quickly.
"We're going to make this individual's world very, very, very small," he said.
Mr Godwin, a father of nine and grandfather of 14, was shot walking home after enjoying an Easter meal with his children.
The hunt for Mr Stephens had been widened to include the states of Pennsylvania, New York, Indiana and Michigan.
The suspect is described as African-American, 185cm tall and 108kg with a full beard.
Police have told Americans to be on the lookout for his car, a white Ford Fusion.
Mr Williams urged people not to contribute to any GoFundMe pages taking donations because they had not been set up by Mr Godwin's family.