The group told reporters at City Hall on Friday that it has serious concerns about the drilling method, called high-volume hydraulic fracturing.
It involves injecting huge amounts of pressurized water into the ground to crack rock and force gas to the surface.
Critics say it can lead to groundwater pollution. They also question the safety of chemicals used during the drilling process.
The Independent Oil and Gas Association of New York says hydraulic fracturing has been used safely in the state for 60 years without any harm coming to drinking water.