Facebook has launched a review into how it handles violent videos and other offensive material, as a nationwide manhunt is under way for an American man who posted a video of a killing to the social media site.

The company said on Monday that it needed to improve after the video of the murder in Cleveland on Sunday remained on its website and mobile app for two hours.

In a statement, the social media platform said it would look for ways to make it easier for people to report such videos and speed up the process of reviewing items once they are reported.

'We prioritise reports with serious safety implications for our community, and are working on making that review process go even faster," said Justin Osofsky, Facebook's vice president for global operations and media partnerships.

The incident was the latest disturbing crime captured on Facebook video in the United States, including the alleged gang rape of a 15-year-old girl, two fatal shootings and the kidnapping and torture of a disabled 18-year-old man.

Facebook relies on its 1.9 billion users to report items that violate its terms of service.

Millions of items are reported each week in more than 40 languages and thousands of workers review them, Osofsky said.

Cleveland killing

Meanwhile, police said that they had received dozens of tips about the possible location of Cleveland suspect Steve Stephens.

Cleveland police, working on the case with help from investigators at the FBI and the US Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF), offered a reward of up to $50,000 for information leading to the Stephens' arrest.

Stephens, 37, of Cleveland, Ohio, who was described as armed and dangerous, was also placed on the FBI's Most Wanted list.

He is wanted on a charge of aggravated murder in the death of Robert Godwin Sr.

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In the video, Stephens gets out of his car and appears to randomly target Godwin, 74, who is holding a plastic shopping bag. Stephens says the name of a woman, whom Godwin does not seem to recognise.

"She's the reason that this is about to happen to you," Stephens tells Godwin before pointing a gun at him. Godwin can be seen shielding his face with the shopping bag.

Facebook said the suspect went live on the social media website at one point during the day, but not during the killing. Police had earlier said that Stephens broadcast the incident live.

The victim's son, Robert Godwin Jr, told Cleveland.com that he could not bring himself to watch the video.

"I haven't watched the video. I haven't even looked at my cellphone or the news," Godwin said. "I don't really want to see it."

He said his father, a retired foundry worker, collected aluminum cans and was probably looking for cans when Stephens approached him.

In a separate video posted on Facebook, Stephens claimed to have killed more than a dozen other people.

"Like I said, I killed 13, so I'm working on 14 as we speak," he said.

Police did not verify any other shootings or deaths.