An effort to stop a grilled cheese and milk shake vendor from moving into the Dag Hammarskjold Plaza across the way from the United Nations has been denied.

In a lawsuit filed in June, a community group charged the Parks and Recreation Department with acting in an “arbitrary and capricious” manner when it turned out the existing eatery and offered the site in the small park located on 47th Street to the New York Milkshake Company. The group, the Friends of Dag Hammarskjold Park, had helped spruce up the park in recent years and wanted to keep the existing eatery.

A state judge, Lewis Stone, ruled Monday that the parks department had an acceptable formula for evaluating bids from four vendors and dismissed the lawsuit. Nonetheless, Judge Stone suggested he would not be surprised if the dispute returned to court. He noted that the city comptroller’s office was displeased with the parks department over the bidding process it used. He hinted that his ruling could settle some of the points that would be raised in a lawsuit by that agency.

“We are very pleased that Justice Stone upheld Parks’ award of the concession to New York Milkshake, and look forward to serving the community with the re-opening of the café at Dag Hammarskjold Park,” a city lawyer, Terri Sasanow, said in a statement by e-mail.

The founder of the Friends of Dag Hammarskjold Plaza, Anne Saxon-Hersh, said the group objected to the new vendor because of concern that it would close and leave behind an empty property.

“The parks department has been awarded an enormous discretionary power to do what it pleases without answering to the very community it serves,” she said. “Yet we are the ones raising money to take care of the park. The biggest battle for us is over concessionary reform.”

The greenhouse-like building where the eatery is to be located now sits empty after the former vendor, the Patio, was ordered out in June to make way for the New York Milkshake Company.

The owner of the company, Scott Marcus, said he intends to open in September. He promised to offer food that is not all that different from what the Patio restaurant once served.

“All that this other guy had was alcohol and hot-dogs,” Mr. Marcus said by telephone. “So what’s wrong with a grilled cheese sandwich and a milk shake?”

Mr. Marcus, who has a store in Battery Park and two counters on tour boats, said he will be paying the city $4,000 a month to use the park.