We need to bring this to a conclusion -- today," Cleveland Police Chief Calvin Williams told reporters during a search for the suspect, identified as Steve Stephens.
"There is no need for any further bloodshed in this incident tonight," Williams added.
Police said late Sunday that Stephens "may be out of state at this time," and authorities called on residents of Pennsylvania, New York, Indiana and Michigan "to be on alert."
Stephens didn't know the elderly victim he killed around 2 p.m., said Cleveland authorities, who did not release a motive.
Stephens also claimed publicly to have committed multiple homicides, according to police. Williams said, "Currently, there are no other victims that we know of."
Authorities said Stephens is a black male who is 6-feet 1-inch and weighs 244 pounds. He has a full beard.
Stephens was last seen wearing a dark blue and gray or black striped polo shirt. Stephens is driving a white Ford Fusion with temporary license plates, according to Cleveland police.
Authorities believe Stephens recently purchased the car.
'What happened today is senseless'
"He is considered armed and dangerous, so we want people to be careful out there," Williams said.
The FBI is assisting Cleveland police in the search for Stephens. Nearly five hours after the shooting, Williams said authorities hadn't had a verifiable report of a sighting of Stephens. Hundreds of leads had poured into the department, police said.
"What happened today is senseless and if Steve has an issue, he needs to talk to some folks to get that resolved," Williams said.