The man suspected of killing a Cleveland man and posting a video of the murder on Facebook fatally shot himself after a "brief pursuit" by Pennsylvania State Police officers on Tuesday, police said.

Steve Stephens was accused of shooting Robert Godwin Sr., 74, on a sidewalk in Cleveland, Ohio, on Sunday before fleeing in a car.

He uploaded the video of the murder to Facebook, becoming the subject of a nationwide manhunt.

Pennsylvania State Police officers found Stephens in Erie County, Pennsylvania, after getting a tip from the public that his white Ford Fusion was parked outside a McDonald's fast-food restaurant.

After a brief chase, Stephens stopped his vehicle, Williams said.

"As the officers approached that vehicle Steve Stephens took his own life," Williams said.

"We would have preferred that it had not ended this way," he added, saying he and the community would have had "a lot of questions" for Stephens.

Stephens, who had no prior criminal record, was not suspected in any other killings, Cleveland officials said.

Stephens said in a separate video on Facebook on Sunday that he had already killed a dozen others.

The shooting marked the latest video clip of a violent crime to turn up on Facebook, raising questions about how the world's biggest social media network moderates content.

Meanwhile the founder of Facebook, Mark Zuckerberg has reacted to the incident.

Zuckeberg while sending condolences to the families of the victims, said his organisation will continue to do all they can to prevent a re-occurrence.