The Electronic Privacy Information Center bypassed lower courts in filing its emergency appeal directly with the nation's highest court.
The group claims a secret federal court improperly authorized the government to collect the electronic records, and contends only the Supreme Court can decide the issues involved, CNN reported.
"Telephone records, even without the content of the calls, can reveal an immense amount of sensitive, private information," group President Marc Rotenberg said. "There are no reasonable grounds for the NSA to have access to every call record of every Verizon customer."
He said the secret surveillance court has applied the law "in a way that is contrary to the text and purpose of the statute."
CNN noted the Supreme Court does not comment on cases before it and the Justice Department could ask for more time to replay, possibly delaying the appeal for months.
The NSA's domestic phone data-mining activities were revealed by former agency contractor Edward Snowden, who the federal government is trying to have extradited from Russia where he has fled while seeking political asylum with a country that won't turn him over to U.S. authorities.