NEW YORK — The official cleanup of a plaza in lower Manhattan where protesters have been camped out for a month was postponed early today, sending up cheers from a crowd that had scrambled to scrub the park on its own out of fear the effort was merely a pretext to evict them.

Deputy Mayor Cas Holloway said the owners of the private park, Brookfield Office Properties, had put off the cleaning. Supporters of the protesters, including union members, had started streaming into the park in the morning darkness well beforehand in a show of solidarity.

There was still skepticism even after the protesters were told they could stay, for now.

“I’ll believe it when we’re able to stay here,” said protester Peter Hogness, 56, a union employee from Brooklyn. “One thing we have learned from this is that we need to rely on ourselves and not on promises from elected officials.”

The protest in New York that began a month ago has spawned similar encampments in cities across the U.S. and world.