The non-profit organisation has also asked the court to issue an initial injunction.
The US National Security Agency’s (NSA) mass surveillance programme is said to be breaching the constitution, according to the American Civil Liberties Union (ACLU).
The non-profit organisation has also asked the court to issue an initial injunction stopping or limiting NSA activity.
It has also warned that such long-term surveillance would enable the government to gather a detailed profile of every person residing in the US, while also drawing a complete sketch of their links with one another.
The court motion, part of lawsuit filed in June, said: "The chilling effect of the mass call-tracking program is apparent: any person hoping to approach plaintiffs with proof of official misconduct would be understandably wary knowing that the government receives, almost in real-time, a record of every telephone call."
ACLU is one of several organisations who opposed the NSA, after disclosures from the Guardian vsaid the NSA had been snooping calls and emails of US citizens.
Recently, the Guardian teamed up with the New York Times to give the US daily access to some of the secret documents disclosed by Edward Snowden.