By Barbara Liston

SANFORD, Florida (Reuters) - Thousands of protesters marched through Sanford, Florida, on Saturday demanding an arrest of the neighborhood watch volunteer who shot and killed an unarmed black teen a month ago.

"We want arrests ... shot in the chest," they chanted, referring to 17-year-old victim Trayvon Martin, who was shot in the chest.

Ben Jealous, president of the NAACP which organized the march, and civil rights leader the Rev. Al Sharpton denied media reports that Sharpton planned to call for an economic boycott of Sanford or the surrounding central Florida area, calling it a "media fabrication."

"Put to rest the rumor that there is any discussion of a boycott of the community," Jealous told reporters.

Demonstrators called for the arrest of George Zimmerman, the 28-year-old neighborhood watch captain who admitted shooting Martin with a semiautomatic handgun. Zimmerman, a white Hispanic, had called 911 to report a "suspicious" person and followed Martin against the dispatcher's advice.

Zimmerman said he shot in self defense during a fight with Martin, and his family have said the reports Zimmerman was the aggressor are misleading and false. Local police declined to arrest Zimmerman citing Florida's "Stand Your Ground" law allowing violence in self defense.

The ensuing public outcry has prompted ongoing state and federal investigations and charges of racial bias.

"We're here to say 'save our sons.' Bring Mr. Zimmerman to justice," Jealous said before the march began.

With gospel music playing in the background, protesters were marching from a technical high school campus through a predominantly black neighborhood to the Sanford Police Station. The throng stretched for blocks, weaving past homes, churches and small businesses, many of them boarded up.

It was one of the largest demonstrations yet in Sanford, where Martin was killed on February 26. Organizers said they were committed to non-violence and noted there had been no arrests or disturbances at any of the marches.

NAACP chapters from South Carolina, Georgia and Alabama arranged buses to bring participants to the rally, while others traveled by car.

"Because of the age of the young man and because of the circumstances of his death, every community can identify with that," said Bernard Simelton, president of the Alabama state conference of the NAACP. "We've had things like that happen in Alabama where somebody gets killed and the police just sweep it under the rug. It just touches everyone."

While insisting there was no call for a boycott, Sharpton said there could still be unspecified action against national corporations that support the "Stand Your Ground" laws like the one police cited when they declined to arrest Zimmerman. The law gives wide latitude to use deadly force when a threat is perceived.

Sharpton declined to identify those corporations but said, "We take nothing nonviolent off the table."

(Additional reporting by Harriet McLeod, writing by Jane Sutton; Editing by Greg McCune)