* Organized labor rejects call for general strike
* Protests in Chicago, San Francisco
* New York police report white powder found in mail
By Edith Honan
NEW YORK, May 1 (Reuters) - Occupy Wall Street sought to breathe fresh life into the movement that sparked a wave of nationwide protests against economic injustice eight months ago with May Day events across the United States on Tuesday and a call for a general strike that went unheeded.
By mid-morning May 1, about 500 activists had gathered at Bryant Park in midtown Manhattan for a "pop-up encampment" emblematic of the movement's early days in lower Manhattan's Zuccotti Park near the Wall Street financial district.
On the Williamsburg Bridge, linking Brooklyn and Manhattan, about 350 demonstrators marched on the pedestrian crossing with signs reading "Capitalism Kills Fun" and "Strike!" Several dozen police accompanied them on foot and on scooters.
In San Francisco, the May Day protests began early on Monday night, when a group of demonstrators walking through the city's Mission District smashed windows and splashed paint on buildings and vehicles near a police sub-station, said police spokesman Sergeant Daryl Fong. Officers arrested one of the protesters.
Occupy Chicago protesters, shadowed by police, gathered outside Bank of America branches, raising a large "Chicago Spring" banner and chanting "Banks got bailed out, we got sold out."
Police blocked a State Street bank entrance, and banks in Chicago's banking center on LaSalle Street prepared for protesters by posting extra guards and closing some entrances.
Other plans for May Day included a march with organized labor starting from New York City's Union Square in the afternoon. In Washington, there were plans to march to the White House.
A text message broadcast late Monday from an Occupy Wall Street address said: "All civilians stand by for GENERAL STRIKE at 08:00. No Work, School, or Shopping. All out in the streets!"
Labor unions rejected pleas for a general strike.
Police in New York declined to say if any unusual security precautions were planned but the city's financial community was making preparations. At the Deutsche Bank building in lower Manhattan, the atrium used for much of the winter as an Occupy meeting spot was closed to the public.
Directly across the street from Bryant Park at the Bank of America tower, about a dozen police blocked access to the building. One person was arrested in the middle of 6th Avenue in front of the skyscraper.
They also targeted the headquarters of Rupert Murdoch's NewsCorp with a group chanting "Fox News: Pay your share!" and demanding Murdoch's arrest.
"The Wall Street fat cats are unfairly gaming the system in a way that makes the common man upset," said Bradley Shields, 56, a freelance travel photographer visiting from Honolulu.
New York police reported 10 instances of white powder being mailed to financial institutions and City Hall on Monday and Tuesday in which a harmless substance was sent along with a note saying, "Happy May Day ... This is a reminder you are not in control."
TARGET: U.S. FINANCIAL POLICIES
Inspired by the pro-democracy Arab Spring, the Wall Street protesters last year targeted U.S. financial policies they blamed for the yawning income gap between rich and poor - between what they called the 1 percent and the 99 percent.
"We have to show the 1 percent what democracy looks like," said Joycelyn Gill-Campbell, an outreach coordinator with Domestic Workers United. "The domestic workers take care of their children, their homes, and they're treated like less than human beings."
It was unclear whether the event would feed a resurgence of Occupy after a winter hiatus.
In New York, the Occupy movement lost significant momentum in November when a pre-dawn sweep broke up the encampment at Zuccotti Park. Occupy protests in Oakland, California, in January led to police firing tear gas into crowds of protesters and more than 200 people were arrested.
Since last fall, when scores of demonstrators set up a vigil in lower Manhattan's Zuccotti Park and Occupy boasted it had $500,000 in the bank, donations have slowed to a point where Occupy was left in a cash crunch earlier this year.
In recent weeks, small groups of New York protesters have taken to camping out in different locations, including across the street from the New York Stock Exchange.