NEW YORK — New York’s City Council pulled the reins on a plan to overhaul Central Park’s popular carriage horse rides Thursday after the drivers’ union withdrew its support, citing concerns the deal threatens the industry’s future.

The Teamsters union said it cannot support a bill — backed by Mayor Bill de Blasio — currently before the Council that would trim the carriage fleet and ban carriage horses from Manhattan streets.

‘‘With the legislation now finalized, our members are not confident that it provides a viable future for their industry,’’ said George Miranda, head of Teamsters Joint Council 16.

The director of the mayor’s office of operations, Mindy Tarlow, said previously that the proposal aimed to strike a balance between eliminating the dangers posed to the horses in traffic while ensuring the viability of the industry.

In return for the new restrictions, the plan would have given the horses a permanent home in a multimillion-dollar Central Park stable, to be built at city expense.

City Council Speaker Melissa Mark-Viverito said the plan was contingent on an agreement between the administration, the Teamsters, and the City Council. A disappointed de Blasio said the Teamsters had backed away from a ‘‘fair compromise they had previously endorsed.’’

Associated Press