Sen. Rand Paul, R-Ky., walked into U.S. District Court in Washington, D.C., Wednesday morning to file a lawsuit against President Barack Obama and various administration officials in his bid to kill the National Security Agency’s dragnet collection of American phone records.

Plaintiffs named in the lawsuit are Paul and the political advocacy group FreedomWorks, which claims about 6 million members.

Ken Cuccinelli, Virginia’s former Republican attorney general, will serve as lead counsel for the lawsuit, which is the fourth major legal challenge against the NSA phone program.

“We don’t do this out of disrespect to anyone,” Paul told a crowd of reporters outside the court, but rather “out of respect for the Constitution.”

Cuccinelli and Paul said they plan to have the lawsuit certified as a class-action representing all American phone users.

More than 386,000 people volunteered as plaintiffs on the website of Paul's political action committee, RAND PAC, in the time since he first announced his intention to sue in June, Paul said.

But those volunteers aren’t named in the lawsuit and Cuccinelli said their role will be merely to serve as “one more important indicator” of public opposition to the NSA’s metadata program.

The people who offered to be plaintiffs were asked for their email addresses by Paul’s group and for donations.

Paul’s lawsuit is narrow in focus, alleging only that the phone program violates the Fourth Amendment and seeking only injunctive relief and the purging of stored records. It does not seek a preliminary injunction, in the hope of speeding up the legal process.

A similar lawsuit filed by conservative legal activist Larry Klayman in June alleges First, Fourth and Fifth Amendment violations and, in addition to seeking injunctive relief, seeks damages.

Klayman won a preliminary injunction against the phone program Dec. 16 from U.S. District Court Judge Richard Leon of Washington, D.C., who found the program is “almost Orwellian” and “almost certainly” violates the Fourth Amendment. Leon stayed his ruling as the Department of Justice appeals.

Klayman and a senior Paul staffer told U.S. News in January that if Paul filed his suit in D.C., rather than in Kentucky, the two anti-surveillance cases might be heard “in tandem,” possibly meaning joint court hearings and a joint ruling.

But Cuccinelli said Wednesday he doesn’t expect the new case to be heard in tandem “with anything else,” even though the cases do contain related subject matter. He declined to speculate on whether the case will be assigned to Leon.

Cuccinelli did predict the case will be a “several years-long process,” ideally concluding with a Supreme Court ruling.

During his remarks to reporters, Paul said there’s no evidence the NSA’s bulk collection of phone records has been effective at catching terrorists and brushed aside seven years of approval from federal judges on the Foreign Intelligence Surveillance Court.

“This is a secret court, [but] the Constitution is a public document,” Paul said. The likely 2016 presidential candidate compared the court’s approval of mass data collection to general warrants issued by British authorities before the American Revolution.

“I’m not against the NSA, I’m not against spying, I’m not against looking at phone records,” Paul said. “If you do it properly [with an individualized warrant] there is no limit” to the number of queries or “hops” through the contacts of targets and the contacts of their contacts, he said.

Paul said he doesn’t believe exiled whistle-blower Edward Snowden, who exposed the NSA surveillance programs with leaked documents, should be called as a witness.

In addition to Paul and Klayman, the American Civil Liberties Union and the Electronic Frontier Foundation are challenging the phone program in New York City and San Francisco federal courts, respectively. Klayman also is suing to halt the NSA's PRISM Internet program.

Read: Paul's NSA Lawsuit: