Auto makers and other companies racing to commercialize self-driving car technology are facing pushback from local politicians, complicating their plans to bring real-world testing to more U.S. cities.

In New York City, General Motors Co. has put on hold plans to begin testing in Manhattan because Mayor Bill de Blasio has expressed concerns about the technology’s safety, according to people familiar with the matter. GM said last year it would be the first company to start driverless-car testing in the city, starting in early...