The de Blasio administration has backed away from its fight with the app company Uber, agreeing on Wednesday to drop for now its plan to place a cap on the number of vehicles Uber operates in New York City.

The move brings a temporary end to a fractious struggle that had consumed City Hall for several days, inundating parts of the city with mailers, phone calls, advertisements and, on Wednesday, broadsides against Mayor Bill de Blasio from familiar faces and an even more familiar foe.

Under an agreement with the company, the city will conduct a four-month study on the effect of Uber and other for-hire vehicle operators on New York’s traffic.

A City Council bill, which was to come to a vote as early as Thursday, had called for a cap on the company’s growth during the study. Officials said that a similar restriction remained a possibility down the line.

The arrangement requires Uber to release a trove of data the city had been seeking for its analysis, officials said.

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Perhaps the company’s most potent new ally, though, was a less surprising mayoral critic: Gov. Andrew M. Cuomo, who waded into the conflict on Wednesday as a staunch defender of the company.

In a radio interview, Mr. Cuomo, with whom Mr. de Blasio is enmeshed in an open feud, called Uber “one of the great inventions of this new economy.”

“I don’t think government should be in the business of trying to restrict job growth,” he said on “The Capitol Pressroom.”

Mr. Cuomo joined a growing list of prominent Democrats who denounced the Council measure, including the city comptroller, Scott M. Stringer, and the Brooklyn borough president, Eric L. Adams.

According to the office of the City Council speaker, Melissa Mark-Viverito, the legislation had the votes necessary to pass. In a statement, she suggested the agreement was a preferable path, saying the goal all along has been “to thoughtfully address the impacts of the explosive growth in the for-hire vehicle industry.”