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.