Robert Stolarik for The New York Times

Young people in knit hats and jeans scurried around Thursday wielding brooms and trash bags, moving mountains of sleeping bags, backpacks and jackets out of the way.

By cleaning up Zuccotti Park on their own, they were trying to persuade the park’s owner, Brookfield Properties, to back down from its plan to send in cleanup crews Friday morning and begin to enforce new rules on the use of the park that would end the Occupy Wall Street protest, at least in its current form.

But as the day wore on, it seemed that the protesters’ efforts to placate Brookfield might, in the end, not matter, and all sides were girding for a Friday showdown. The police said they were ready to step in if the company asked for help in removing protesters or enforcing the new rules, while protesters planned to form a human chain around the park and, using Facebook and Twitter, called on sympathizers to join them.

Some protesters saw the cleanup as tantamount to an eviction notice, and they vowed to stand their ground, even if it meant being arrested. “This is a public park privately held — I don’t even understand what that means,” Travis Nogle, a 32-year-old protester and “earthship builder” from San Francisco said as he changed his shoes and prepared to pitch in with the cleanup. “We have a constitutional right to protest.”

Ozier Muhammad/The New York Times

Zuccotti Park, a plaza that takes up an entire downtown block, is owned and maintained by Brookfield but open to the public. While the police have confronted and arrested demonstrators during marches in the streets and on the Brooklyn Bridge, they have largely left the Zuccotti Park protests untouched, allowing the people there to camp out around the clock while ringing the park with barricades and dozens of officers.

But in a letter to the police commissioner, Raymond W. Kelly, this week, the company’s chief executive, Richard B. Clark, said that sleeping protesters were blocking walkways “at all hours of the day and night.” The letter said that there had been neighborhood complaints of “lewdness, groping, drinking and drug use” and that the company had not been able to perform its daily maintenance.

“We fully support the rights of free speech and assembly,” he wrote, “but the matter in which the protesters are occupying the park violates the law, violates the rules of the park, deprives the community of its rights of quiet enjoyment to the park, and creates health and public safety issues that need to be addressed immediately.”

The company circulated a notice in the park Thursday explaining its plan: it would clean a third of the park at a time, allowing protesters to return to each section once the job was done. More important, however, was the company’s vow to enforce new rules that it imposed after the protest began about a month ago, which seem aimed at the very essence of the occupation: no camping, no tents, no tarps, no sleeping bags, no lying on the ground or on benches, and no storage of personal property on the ground or walkways “which unreasonably interferes with the use of such areas by others,” the company said in its notice.

While demonstrators tried to tidy up the park Thursday — at one point a power washer was obtained, but there was no water available to pump through it — Scott M. Stringer, the Manhattan borough president, called on City Hall officials to try to reach a deal with the protesters. And the New York Civil Liberties Union issued a statement, saying: “The city must not use the cleanup as a pretext for mass arrests. To do so would be a violation of the spirit of the First Amendment and the spirit of dissent.”

Thirteen City Council members wrote in a letter to Mayor Michael R. Bloomberg that they supported a cleanup, but added, “The new rules you are enforcing, however — in particular the prohibition on sleeping bags and gear — is an eviction notice and potentially an unconstitutional closing of a forum to silence free speech.”

Ozier Muhammad/The New York Times

But Brookfield, in a statement, seemed intent on carrying out its plans: “As sections of the park are cleaned, they will re-open to the public. All are welcome to enjoy the park for its intended purpose as an open neighborhood plaza, in compliance with posted rules.”

City Hall issued its own statement Thursday afternoon, standing behind Brookfield’s decision to clean its own park and demand that protesters abide by their rules. “We will continue to defend and guarantee their free speech rights, but those rights do not include the ability to infringe on the rights of others, which is why the rules governing the park will be enforced,” said Marc La Vorgna, a spokesman for Mr. Bloomberg.

Some protesters have pointed out that the mayor’s longtime girlfriend, Diana L. Taylor, is on the board of directors of Brookfield.

According to Jerold S. Kayden, a lawyer and professor of urban planning and design at Harvard University and an expert on private parkland, New York City gives the owners of public spaces like Zuccotti Park the right to impose “reasonable” rules of conduct. While many private parks and plazas have nighttime curfews, Zuccotti and others — created under an earlier zoning law — are generally required to be open to the public at all times. “I would suspect that the city might view rules against sleeping overnight and permanent occupation to be reasonable,” he said. “But reasonableness is in the eye of the beholder.”

Still, the Occupy Wall Street demonstrators held out hope they could forestall the Brookfield cleanup by taking care of their own sanitation. The cleanup efforts were slow at first, with only a handful helping in the morning.

“Every action you see here is autonomous,” said Fred Pantozzi, a protester filling plastic bags with trash.

“Autonomous enough for people not to be doing it,” added another protester, Henry Perkins, a 21-year-old student at the University of Alabama.

Gradually, however, more people heeded the call. Volunteers taped off sections of the park, hauled off debris and scrubbed walkways clean.

Some said that if the police took away their sleeping bags they would sleep in the park sitting up.

A girl in a purple plaid jacket and short skirt said this was not a good idea. “If we stay up all night without sleeping bags we’re going to get sick and we’re going to look crazy on TV,” she said. “Activist burnout is a real thing. If you can take one night to sleep at a friend’s house and rest up.”

Mr. Perkins was putting abandoned clothing into clear plastic bags. He said he had not had a shower in five days, but somehow managed to keep fairly clean. He hoped the protesters would not be evicted. “My autonomous plan is to wake up before they get here and to be out of the way,” he said. “I will move quadrant by quadrant. I hope they don’t kick us out.”

Reporting was contributed by Lisa W. Foderaro, Rob Harris, Meredith Hoffman and Colin Moynihan.