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The collection of phone records started under the George W. Bush administration but did not come to light until last year when former government contractor Edward Snowden leaked details to the press.

Larry Klayman, a conservative activist, filed a pair of lawsuits against the Obama administration last summer. In December, he scored a victory when U.S. District Court Judge Richard Leon ruled that the NSA must stop collecting and retaining the phone records of Mr. Klayman and his co-plaintiff.

Judge Leon stayed his order, though, pending an appeal from the Justice Department.

Soon afterward, a federal judge in New York ruled in favor of the NSA program, turning back a constitutional challenge from the American Civil Liberties Union.

Judges who sit on the secret Foreign Intelligence Surveillance Court have approved the program repeatedly, though they occasionally have added restrictions and issued warnings when they thought the government was overstepping its boundaries.

Since winning before Judge Leon, Mr. Klayman has filed another class-action lawsuit that is broader in scope than Mr. Paul’s case.

That lawsuit challenges the government’s data mining program known as Prism. It also challenges Section 215 of the Patriot Act, which grants the government the power to collect records from businesses.

Mr. Paul on Wednesday dismissed reporters’ political questions, but the lawsuit and government snooping programs overall likely will be issues in the 2016 presidential race.

But Mr. Klayman said the politics showed in the way that complaint was written.

“It is very peculiar in that the allegations seem to be watered down,” he told The Washington Times. “It is more of a political document. In any event, as I said, we are pleased finally that Paul is entering the fray. That is fine, but we would like them to accurately reflect that there is another class action out there that was filed much sooner than him. But we welcome his participation and anyone’s participation.”