A three-year construciton project is slated to begin at 58th Street in July.
Construction of new park space at Asser Levy Place will begin in two weeks, bringing new traffic rules.
J.D. Carlisle told CB6 it would yank its support for another project unless the market was pushed out.
The plaza is too close to the United Nations and too popular among protesters and tourists, they say.
Of the 53 proposed sites, 22 bike-share stations would require the loss of public or commercial parking.
Several Tudor City residents are pushing to turn an East 43rd Street cul-de-sac into a public plaza.
At a meeting on Monday night, members of Community Board 6 voted to approve the co-naming of East 21st Street after NYPD Officer Glen Pettit, who died on 9/11.
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