A City Council vote on the future of Central Park’s horse-drawn carriage industry has been called off after the Teamsters union negotiating on behalf of the carriage drivers announced Thursday morning it is withdrawing its support of a compromise bill.

The vote had been set for Friday on a deal that would reduce the number of working horses by roughly half to 95 and move the industry to a stable to be built by the city within the park. Many council members expressed frustration with Mayor Bill de Blasio’s administration after a hearing last month when his aides struggled to answer questions about details of the plan.

Teamsters Joint Council 16 president George Miranda said Thursday morning that the deal between his union, de Blasio and City Council Speaker Melissa Mark-Viverito is not in the drivers’ best interests. The parties had acknowledged that dozens of drivers would lose their jobs.

“With the legislation now finalized, our members are not confident that it provides a viable future for their industry,” Miranda said in a statement. “We cannot support the horse carriage bill currently before the City Council.”

De Blasio and Mark-Viverito in separate statements defended the negotiation process.

The mayor said the parties will work “toward a new path” on the industry he had vowed to ban as a key campaign promise in 2013.

“We negotiated in good faith with the City Council and the Teamsters to reach this agreement,” de Blasio said. “The terms of that agreement have not changed during these past weeks, but today the Teamsters decided to back away from the fair compromise they had previously endorsed.”

Mark-Viverito said the bill “was contingent on an agreement between the administration, the Teamsters and the City Council. The Council will not vote on any horse carriage related legislation on Friday since the Teamsters no longer support the deal.”

The compromise bill also drew criticism from some animal welfare groups seeking an outright ban as well as pedicab operators who were not part of the negotiations but who would have been prohibited from working in the park’s tourist-heavy southern sector under the deal.

Council aides said the speaker had enough votes to pass the bill on Friday, but the vote will not take place because the deal was predicated on agreement.