The suspect, Steve Stephens, said in another video post that he had killed 13 people and would kill more.
He shot dead 74-year-old Robert Godwin as the victim reportedly walked home from Easter lunch on Sunday afternoon.
Police have asked residents of Ohio, Indiana, Michigan, New York and Pennsylvania to be on the alert.
Cleveland police department have issued a photo of Mr Stephens, 37, on its website, describing him as a black male, 6ft 1in (1.9m) and 244lb (110kg).
He is thought to be driving a white Ford Fusion, but may have switched cars.
They said that Mr Stephens, who has a licence to carry a concealed firearm, is probably still armed and dangerous.
Nine schools in Philadelphia were placed on lockdown on Monday after police received multiple calls reporting a possible sighting of Mr Stephens.
Police have yet to verify the reports.
His mobile phone signal was last tracked on Sunday afternoon in Erie, Pennsylvania.
Cleveland Police Chief Calvin Williams said in a press conference on Monday morning: "Steve is still out there some place… we're still asking Steve to turn himself in, but if he doesn't we'll find him."
FBI Special Agent Stephen Anthony said: "Quite frankly, he could be in a lot of places." >>>>
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