For-hire drivers in the city, many of whom are nonwhite immigrants, are being hurt because the roads are oversaturated with vehicles, Ms. Desai said. Ride-hailing vehicles and yellow taxis were empty a third of the time while in Manhattan’s central business district, according to the 2017 report by Bruce Schaller, a former city transportation official.

“Defending the oversaturation which has resulted in the deep poverty of a work force made up of immigrants of color is not a civil rights position, it is the antithesis,” Ms. Desai said.

This is the second time the city has sought to slow the growth of for-hire vehicles. Mayor Bill de Blasio proposed a cap on for-hire vehicles in 2015, but the city backed down after Uber waged a public-relations campaign. Mr. de Blasio voiced support on Friday for the most recent proposal.

Uber has started a social media campaign against the proposed license freeze, and this year created a website that emphasizes the number of trips “in areas long ignored by yellow taxis and where access to public transit is limited.”

“We are growing fastest in the outer rings of the outer boroughs because we are serving communities that have been ignored by yellow taxis and taken for granted by the M.T.A.,” said Josh Gold, a spokesman for Uber, referring to the Metropolitan Transportation Authority.

Uber statistics, he said, show that ridership in neighborhoods such as East New York in Brooklyn and Kingsbridge in the Bronx had more than doubled since this time last year.

Mr. Sharpton and Ms. Rice say their nonprofits have received donations from for-hire companies such as Uber and Lyft. The taxi industry has donated money to the campaigns of Mr. de Blasio and members of the City Council, including Rubén Díaz Sr., chairman of the Committee on For-Hire Vehicles.