NEW YORK (CBSNewYork) – The City Council is postponing a vote on a bill to restrict horse-drawn carriages to Central Park after the Teamsters Union withdrew its support, citing concerns about their jobs.

The vote on the compromised plan, which was initially supported by the union, Mayor Bill de Blasio and City Council Speaker Melissa Mark-Viverito, was set to take place on Friday.

But the Teamsters announced Thursday that they can’t support the bill in its current form.

“The Teamsters’ first priority is always our members and their livelihoods,” said George Miranda, president of Teamsters Joint Council 16 which represents the horse-drawn carriage workers. “With the legislation now finalized, our members are not confident that it provides a viable future for their industry. We cannot support the horse carriage bill currently before the City Council.”

Mark-Viverito said the bill “was negotiated in good faith and 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 proposal called for several changes, including reducing the number of licensed horses and limiting them to Central Park where the animals would live in tax-payer funded stables.

It also included a ban on pedicabs from operating in Central Park below 85th Street.

“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. While we are disappointed this bill will no longer be considered Friday, the people of this city know what I believe, and we will work toward a new path on this issue.”

The mayor told reporters on the steps of City Hall that although he’s disappointed with the decision from the Teamsters, he’s confident they will “find a way forward” on the issue.

“We had a good faith agreement with them that was worked on for many weeks, and they didn’t keep their agreement its a simple as that,” de Blasio told CBS2’s Dick Brennan.

Queens City Councilman Jimmy Van Bramer, however, gently urged the mayor to move on.

“This has been talked about for a very long time and I think it’s wise to move on at this point,” Van Bramer told WCBS 880’s Marla Diamond.

Some carriage drivers at the West 52nd Street stables said they were relieved that the vote was called off.

“The people in our business have had this hanging over us since the day Mayor de Blasio got elected and hopefully, this is the end of it,” one driver told 1010 WINS’ Glenn Schuck. “I think it’s just an unbelievable sense of relief.”

Steve Nislick and Wendy Neu, founders of the animal advocacy organization NYCLASS, issued a statement condemning the decision to postpone the vote.

“The Speaker’s decision to continue to place carriage horses in harm’s way is outrageous and wrong,” the statement said. “Let’s be clear about what this cold-hearted delay means — horses will continue their miserable nose-to-tailpipe existence, horses will continue to be hit and killed by city traffic, horses will continue to work until they are the equivalent of 80-years-old, and horses will continue to be sold to slaughter.”

They called the proposal “a sensible plan to protect the horses” and said “it deserves a vote.”

“But instead the Speaker is allowing the Teamsters to call the shots and allow the horses to suffer. NYCLASS and our members will never stop fighting to improve the lives of these horses, and will only increase our efforts until the horses win,” they said. “The people of New York deserve to know who stands with the horses and who stands with an industry that has little regard for the well-being of the horses beyond making sure they can make them money, only to toss the horses aside when they can’t.”

While running for mayor, de Blasio promised to ban the carriage horse industry and proposed replacing them with electric cars. That plan was met intense opposition and further efforts to address the issue also faltered.