A black political group offered a $10,000 reward Saturday for the killer of an African-American teenager, amid a nationwide uproar which has prompted a rethink of America's race issues.

The New Black Panther Party displayed a wanted poster on its website with a picture of George Zimmerman, the neighborhood watch volunteer who shot Trayvon Martin, 17, last month.

"WANTED!!! For the murder of Trayvon Martin... ALIVE, not dead or harmed," the poster read.

Several dozen supporters of the group known by its acronym NBPP – unrelated to the revolutionary Black Panther Party active in the 1960s-1980s – meanwhile protested for the third time this week at the police headquarters in Sanford, Florida.

"An eye for an eye, a tooth for a tooth," leader Mikhail Muhammad told the Orlando Sentinel. "We don't hate anyone, we hate injustice."

Activists had called for the mobilization of 5,000 black men to capture Zimmerman. And Muhammad said the NBPP was receiving donations from black entertainers and athletes, with a goal to collect $1 million by next week.

Thousands of demonstrators have marched in at least 10 US cities to express their outrage over the attack, with some of the anger directed at local authorities handling the murder investigation.

They have not arrested or charged Zimmerman because he claimed self-defense, which allowed him to benefit from Florida's "Stand Your Ground" law that lets state residents use lethal force when they are at risk of being killed or seriously injured by an assailant. Zimmerman had a permit to carry a gun.

In Washington, at least 1,000 protesters – many in black hoodies, some with bags of Skittles candy like the one Martin bought before he was shot – gathered at Freedom Plaza in the heart of the US capital to demand justice.