"He could be nearby. He could be far away or anywhere in between," FBI agent Stephen Anthony said on Day 2 of the manhunt for Steve Stephens, a 37-year-old job counselor for teens and young adults.
Police said Stephens killed Robert Godwin Sr., a 74-year-old former foundry worker, on Sunday.
Investigators said that Godwin was the only victim so far linked to Stephens, despite the suspect's claim in a separate video on Facebook that he killed over a dozen people.
Officers searched dozens of places around the city and spoke with the suspect by cellphone, police said.
Police Chief Calvin Williams warned residents to be careful as the go about their day.
Authorities also warned people in Pennsylvania, New York, Indiana and Michigan to be alert for Stephens, who was wanted on a charge of aggravated murder.
Law enforcement officials said that the last place his cellphone signal was tracked was in Erie, Pennsylvania, about 100 miles (160 kilometers) east of Cleveland, on Sunday afternoon.
And nine schools were locked down Monday in Philadelphia, a more than six-hour drive from Cleveland, as police investigated possible sightings of Stephens.
Godwin apparently was shot while out picking up cans in a plastic shopping bag, his daughter said.
"Not because he needed the money, it was just something he did," said 52-year-old Debbie Godwin. "That's all he was doing. He wasn't harming anyone."
She said her father, who had 10 children, was a gentle man with nothing mean about him. "We called him the junk man," she said. "He'd pick up things off the street and fix them. He picked up bikes and he fixed them."
The motive for the shooting wasn't entirely clear from the shaky video, in which Stephens told Godwin a woman's name and said, "She's the reason that this is about to happen to you." Godwin did not seem to recognize the woman's name.
The suspect then pointed a gun at Godwin, who shielded his face with the plastic bag.
The woman Stephens mentioned, Joy Lane, said in a text to CBS that "we had been in a relationship for several years. I am sorry that all of this has happened."
She also said Stephens was "a nice guy" who was generous to everyone and was "kind and loving" to her and her children.
Facebook said the video was posted after the killing but wasn't broadcast on Facebook Live as police initially indicated. The suspect did go live on the social media site at another point Sunday.
The video of the killing was on Facebook for about three hours before it was taken down. Stephens' Facebook page also was eventually removed.
"This is a horrific crime and we do not allow this kind of content on Facebook," the company said. "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."
In the separate video, Stephens said: "I killed 13, so I'm working on 14 as we speak."
Police said they have not verified any other shootings or deaths.
Stephens worked at Beech Brook, a behavioral health agency headquartered in Pepper Pike, near Cleveland. He helped young people develop job skills and find employment, said Beech Brook spokeswoman Nancy Kortemeyer.
An extensive background check before he was hired turned up nothing worrisome, she said.
"We just hope Mr. Stephens is apprehended as quickly as possible so that no one else is injured," she said.
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."