The senator also argued that there's "no evidence" that NSA surveillance of phone data has stopped terrorism, even as the agency's proponents say it plays an important role in keeping the country safe.
Reports over the weekend indicated that the NSA takes information only from 20 percent of American calls, or less -- a lower figure than previously thought.
But Paul noted that the point is not how many percent NSA took, but whether or not you still collect millions of people's information with a single warrant.
In response to the lawsuit, the Justice Department said Wednesday that the telephone metadata programme is legal, as at least 15 judges have previously found.
Paul has been publicly promoting the lawsuit for weeks -- an effort that appears to also be helping him build a campaign infrastructure for 2016, when he's up for re-election to the Senate and when the White House is in play.
