The groups range from the Vermont-based New England Coalition to Washington-based Beyond Nuclear to California's San Luis Obispo Mothers for Peace.
The groups want a more thorough look at risks of fire and leakage at the expanding dry cask storage sites for highly radioactive nuclear waste at reactors around the country.
They want a moratorium on licensing and relicensing of reactors until the risks are resolved.
The Wednesday federal court filing from the two states is part of a process by the NRC that is soliciting comments on nuclear waste storage.
Vermont is home to one nuclear power plant -- Vermont Yankee in Vernon. New York hosts six reactors at four locations.
Last June, a federal appeals court said the NRC should complete a detailed environmental review of on-site storage or explain why one is not needed.
In their filing, the states argue the NRC should consider whether licensing and relicensing reactors makes sense in light of the long-term effect of onsite spent fuel storage.