LOS ANGELES (Reuters) - Police in Long Beach, California, searched on Monday for an unknown assailant who set a man ablaze by tossing a Molotov cocktail at the victim outside a grocery store in a fiery attack caught on videotape.

The 54-year-old victim, who was hit with the incendiary device while sitting on a sidewalk outside the market waiting for his father to do his shopping, was listed in critical but stable condition with severe burns to his body, police said.

The Friday evening attack in an ocean-side Long Beach community, south of Los Angeles, appeared initially to be a random act of violence, authorities said.

"There's no motive that we're aware of at this point, but of course it's still under investigation," police spokeswoman Nancy Pratt told Reuters.

In chilling footage captured by a surveillance camera and posted on YouTube by the Long Beach Police Department, the victim is seen sitting on the ground with his back against the front wall of the market, his legs outstretched, when he is suddenly engulfed in a ball of flame as another man runs past.

The victim then runs out to the parking lot where bystanders rush to his aid and help douse the flames. Another onlooker is seen helping a woman pull her baby stroller out of harm's way near the flames. Police said none of the bystanders were harmed.

Eyewitnesses told police they saw the suspect ignite a bottle of flammable liquid before throwing it at the feet of the victim.

Police released a description of the suspect, a man 25 to 30 years of age, and asked for the public's help in locating him. Pratt said there was no known relationship between the victim and his attacker.

(Reporting by Steve Gorman; Editing by Dan Whitcomb and Todd Eastham)