The New York app, called the Universal E-Hail app, was proposed by councilman Ben Kallos and would be created by the Taxi & Limousine Commission if it receives approval, CNN Money reported.

"City taxis need an app of their own to compete, and New Yorkers need to be able to get a cab in the rain without having to worry about surge pricing," Kallos said. "I want to live in a city where I can e-hail a yellow or green cab and get where I need to be in a New York minute."

The idea of new ride-hailing apps in the two cities comes at a time when Uber and Lyft face problems overseas and at home. Uber is currently banned in Spain and China, and it was recently sued by authorities in Portland, Oregon that demanded for the company to comply with local laws. Both Uber and Lyft were sued by California for allegedly misleading people about its background checks for its drivers.