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Joshua P. Rechnitz, the reclusive philanthropist behind the project, said on Wednesday that he and his team had withdrawn their proposal for the park and would seek another location in or around the city for the indoor sports complex.

For cyclists, it is a velodrome dream deferred. For some Brooklyn residents, who balked at the use of an outsize park parcel for a niche sport, it is good riddance.

But in the end, supporters said, the neighborhood was just too expensive.

The decision to abandon the Brooklyn park, reached at a meeting on Monday, came after planners were unable to produce a design that could fit within the bounds of Mr. Rechnitz's $50 million pledge for its construction and maintenance, despite months of efforts.

"You can't build a facility of this nature, at this site, at this budget," said Greg J. Brooks, the executive director of N.Y.C. Fieldhouse, the nonprofit group behind the project. "We're very excited and eager to find a new home for this recreation center and velodrome. The funding remains intact."

The money came from Mr. Rechnitz, 47, in what is among the largest individual gifts in the history of New York City's parks. A central requirement of the gift had been the inclusion of the bicycle racing track in the complex.

"The New York metropolitan area deserves a world-class cycling and recreation center," Mr. Rechnitz said in a statement on Wednesday. "I greatly regret that this cannot happen in Brooklyn Bridge Park, but I am confident that we will find a new home for the field house in the very near future."

Some Brooklyn Heights residents who live near the proposed site, at Furman Street near Pier 5, had objected to the size of the building and its potential effect on traffic and parking. Others chafed at the notion that a millionaire could, with a large donation, impose an obscure sport on a city park.

But Mr. Brooks, a former deputy comptroller for the city, said it was the costs arising from the site, rather than any local opposition, that had killed the deal.

For instance, the location meant that the roof of the building — visible to those walking above on the Brooklyn promenade nearby — had to be "aesthetic," he said, driving up the price.

Hurricane Sandy also raised concerns about the low-lying site, which did not flood during the storm but sits only about a foot above where the waters came. "A foot doesn't give a lot of room for comfort," Mr. Brooks said, adding that the plan called for raising the structure a few feet off the ground.

The nonprofit organization, he said, had also agreed to provide a boathouse and maintenance for the complex.

The design had been scaled back, reducing the size of the building to 95,000 square feet from 120,000 square feet, and the number of fixed spectator seats to 500 from 2,499, Mr. Brooks said. But even with those changes — and an added $10 million from Mr. Rechnitz for the reserve fund on top of his original $40 million pledge — the project remained stubbornly in the red.

There was no talk of the park making up the difference in the overruns, said Regina Myer, the president of the Brooklyn Bridge Park Corporation.

"We are grateful that we were considered for this facility, and frankly we are saddened that it won't come to fruition in the park," Ms. Myer said.

Ms. Myer said that before Mr. Rechnitz's gift, the site, now occupied by a one-story concrete warehouse, had been planned as a garage for park-maintenance equipment, as a storage area for recreational boats and as restrooms. Officials were looking to return to that plan, she said.

Mr. Rechnitz, a media-shy philanthropist, art collector and cyclist, had considered locations in New York and New Jersey before settling on the Brooklyn park. Many of those locations would be considered again, Mr. Brooks said.