The Bloomberg administration is stepping up its efforts to erect a 35-floor U.N. office tower on Robert Moses Playground, but the community, which says it is starved for open space, is putting up a fight over the 1.3-acre concrete square.

Earlier this week, city officials presented a new plan at a community board meeting that would create a new ball field, jutting out over the East River around 38th Street, to host the roller hockey leagues and other activities that would be affected by the development.

Initially, local residents and elected officials said a planned waterfront esplanade to be built by the city, which would be almost three times larger than the current park space, would not be a viable land swap for the 66-year-old asphalt park. They said it would not provide recreation space for the sports leagues that currently call the small playground home.

“If we lose Robert Moses, there will be only one ball field in the area,” the chairman of Community Board 6, Lyle Frank, said in an interview yesterday.

The city’s new proposal, however, gained more traction with the community Tuesday night. Details of the plan have yet to be fully hashed out, but Mr. Frank said the Parks Department agreed to present the community board with renderings of the substitute ballpark soon. A spokesman for Mayor Bloomberg, John Gallagher, said “the administration agrees with the community regarding the need for open space in the area,” and that Mr. Bloomberg would be working toward “a plan that works for everyone.”

Even if the new development plan wins community support, it could meet resistance at the state level. “The U.N. keeps themselves locked up in that little tower of theirs with no transparency or accountability,” a state senator, Martin Golden, said in an interview yesterday. “As long as that’s going to persist, there’s no reason for the state to do anything for them.”

Any plan that involves a loss of city parkland requires the Legislature’s approval.

Yesterday, Mr. Bloomberg met with the new secretary-general of the United Nations, Ban Ki-moon, at the United Nation headquarters at Turtle Bay, but the subject of the new tower was not discussed, according to an undersecretary-general, Alicia Barcena.

Mr. Bloomberg’s first push to build a United Nations building on the playground site was killed by the Legislature in 2005. Developing the park space is back on the table now, as Deputy Mayor Daniel Doctoroff seeks to build an office tower that would consolidate United Nations offices that are scattered throughout the city, for which many diplomatic tenants pay below-market rates.

The local City Council member, Daniel Gardonick, and other elected officials who represent the Upper East Side last week penned a letter to Mr. Doctoroff, expressing their view that any discussion of developing a United Nations office tower had to take place in the context of a larger redevelopment plan, and include the pending rezoning of the site of the former Con Edison Waterside plant for residential and commercial use, and the renovation of the Franklin Delano Roosevelt Drive, including plans to move a ramp 20 feet west to open up waterfront park space in one of the densest neighborhoods in town.

Tuesday night’s meeting, which drew more than 70 community members, as well as state senator, Liz Kreuger, and Mr. Doctoroff’s chief of staff, Mark Ricks, marked the first time that city officials said they would tackle the various development projects in the area as pieces of a comprehensive development plan for the neighborhood, rather than as individual projects.

“There’s new opportunity for collaboration between the community and the city,” Mr. Gardonick, said.

The open space that has riled up the community is a nondescript concrete square at 42nd Street and First Avenue. But in a dense part of town that has only 26-acres of open space across almost 180 city blocks, elected officials say that every small park is vital to the neighborhood. “To take an existing park from this neighborhood before providing equal or better green space would be a serious blow to the community,” Rep. Caroline Maloney said via e-mail.

“The community was happy that for the first time, the city was saying they want to address all the various development projects comprehensively, rather than piecemeal,” a spokeswoman Ms. Krueger, Sarra Hale-Stern, said.