Hundreds of Occupy Wall Street demonstrators streamed into a desolate part of Foley Square on Saturday afternoon, but their slow-moving march turned chaotic as a phalanx of police officers issued orders to vacate the sidewalks — and then swept in to force the issue.

One police official said that at least 20 protesters were arrested in a series of fast-moving encounters with officers outside the public square in Lower Manhattan that is hemmed in by several government buildings: the State Supreme Court building, a United States courthouse and 26 Federal Plaza, where the Federal Bureau of Investigation has its New York headquarters.