Represented by Electronic Frontier Foundation (EFF), these organisations include Unitarian church groups, gun ownership advocates, and a broad coalition of membership and political advocacy organisations.
This is the first lawsuit filed against NSA after Edward Snowden, a former CIA contractor, leaked to the media details of the secret American program on tapping into the phone details of American nationals and intrusion into private emails of foreign nationals.
In the lawsuit filed yesterday, the plaintiffs have accused the US Government of violating their right of association by illegally collecting their call records.
He said that illegally obtaining such information - especially in a massive, untargeted way over a long period of time - violates the Constitution.
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According to an EFF press release, the thrust area of the suit is the bulk telephone records collection program that was confirmed by publication of an order by Foreign Intelligence Surveillance Court (FISC).
The Director of National Intelligence (DNI) and government officials further confirmed that this formerly secret document was legitimate and just one of series of orders issued on a rolling basis since at least 2006, it said.
"People who hold controversial views - whether it's about gun ownership policies, drug legalisation, or immigration - often must express views as a group in order to act and advocate effectively," said Cohn.
Telephone records, especially complete records collected over many years, are even more invasive than membership lists, since they show casual or repeated inquiries as well as full membership," he said.
There was no immediate reaction from the US Department of Justice.