Sen. Rand Paul on Wednesday announced what he described as one of the largest class-action lawsuits in history, taking President Obama and top intelligence officials to court over National Security Agency surveillance.

"This, we believe, will be a historic lawsuit," the Kentucky Republican said. The suit, joined by conservative advocacy group FreedomWorks, was filed in U.S. District Court in the District of Columbia.

It alleges that the NSA program that sweeps up and stores massive amounts of telephone "metadata" -- which includes where and when calls are made, but not the contents of the calls -- violates the Fourth Amendment. The suit asks the court to rule the program unconstitutional and forbid the government from continuing it.

"There's a huge and growing swell of protest in this country of people who are outraged that their records would be taken without suspicion, without a judge's warrant and without individualization," Paul said, at a press conference in Washington.

He said hundreds of thousands of people have joined, and predicted the suit could "conceivably represent hundreds of millions of people who have phone lines in this country."

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The administration has insisted that Americans' privacy is protected under NSA programs, and Obama recently announced a set of proposed reforms to rein in NSA surveillance.

"We remain confident that the program is legal, as at least 15 judges have previously found," a Justice Department spokesperson said Wednesday, referring to prior court decisions in separate cases.

But the lawsuit argues that the bulk metadata that is routinely collected nevertheless "reveals a wealth of detail" about Americans' personal and professional associations "that are ordinarily unknown to the government."

The suit named Obama, Director of National Intelligence James Clapper, NSA Director Keith Alexander, and FBI Director James Comey.