Uber, setting the stage for what could be another fierce fight, immediately blasted the proposal, arguing that it would hurt its customers, especially those who live in the boroughs outside Manhattan, where the growth of ride-hailing services in neighborhoods ill served by public transit helped them achieve a milestone and surpass yellow cabs in the number of daily riders.

“The City Council’s Uber cap will leave New Yorkers stranded while doing nothing to prevent congestion, fix the subways and help struggling taxi medallion owners,” said Josh Gold, a spokesman for Uber. “The Council’s cap will hurt riders outside Manhattan who have come to rely on Uber because their communities have long been ignored by yellow taxis and do not have reliable access to public transit.”

Mr. de Blasio’s office worked with the City Council on the proposals and Eric Phillips, a spokesman for the mayor, said City Hall would monitor the legislation and hoped that it would help drivers and decrease congestion.

“The mayor was out front on this issue when few people were,” Mr. Phillips said in a statement. “He is pleased it’s getting the attention it deserves from the Council.” Any bill passed by the Council to regulate ride-hailing services would have to be signed by Mr. de Blasio before taking effect.

This week, transit officials said the popularity of Uber and other ride-hail apps had been a factor in the continuing decline in subway and bus ridership. But some transit advocates say the main reason riders are abandoning the subway and bus system is because of terrible service: Uber is just offering an attractive alternative.

The City Council is also moving to regulate Airbnb, another tech company that has upended a long established industry — in this case, hotels. Uber’s leaders have signaled that they were open to discussing new regulations, but they have adamantly opposed any cap.

On Thursday, as city officials began to discuss the cap, Uber released a new ad to oppose the proposal. The ad focused on the difficulty some New Yorkers — particularly people of color — face in hailing a taxi. It shows vehicles vanishing from the app. “If the New York City Council gets its way, all of this could disappear,” the ad says.