The administration of Mayor Bill de Blasio, whose campaign relied heavily on contributions from the yellow cab industry, signaled on Thursday that it would slow the growth of a rival taxi fleet intended to expand street-hail service outside Manhattan.

The new fleet, known as green cabs for their color, was introduced last year under the Bloomberg administration and has proved a popular way for New Yorkers to travel in parts of the city where yellow taxis rarely go.

But the green cabs have been vigorously opposed by the powerful yellow-taxi industry, which stands to face more competition. The industry’s leaders were among Mr. de Blasio’s biggest contributors and fund-raisers in last year’s mayoral race, infusing his campaign with more than $300,000.

The city had been authorized to issue permits for 6,000 additional green cabs beginning in June, adding to the 5,081 already on the streets.