Paul said the National Security Agency and the Central Intelligence Agency have run amok. The intelligence world, he said, had wrongly interpreted that "equal protection means Americans should be spied upon equally."

He demanded stronger oversight, calling for a new, bipartisan select committee to monitor the nation's intelligence agencies. "It should watch the watchers," he said.

"If you have a cell phone, you are under surveillance," Paul warned an auditorium of more than 350 at the University of California (Berkeley), adding, "I believe what you do on your cell phone is none of their damned business."

BERKELEY, Calif.—Sen. Rand Paul delivered a blistering critique of America's spy agencies on Wednesday, likening the surveillance state to the "dystopian nightmares" of literature and arguing that a growing number of his colleagues on Capitol Hill now fear an intelligence apparatus that is "drunk with power."

"I oppose this abuse of power with every ounce of energy I have," Paul declared.

His sharp denunciations received a warm welcome from students and others gathered. Despite the university's famously liberal bent, Paul faced a friendly crowd that included many college Republicans. They greeted him with a standing ovation before he spoke and interrupted his speech repeatedly with applause.

Paul invoked the misdeeds of America's intelligence agencies during the civil-rights movement to make his case for restraint today.

"I find it ironic that the first African-American president has, without compunction, allowed this vast exercise of raw power from the NSA," Paul said. "Certainly, J. Edgar Hoover's illegal spying on Martin Luther King and others in the civil-rights movement should give us all pause."

Paul's address brought some big-name Democrats into the crowd, including former Clinton Labor Secretary Robert Reich and California Lt. Gov. Gavin Newsom. "I'm interested in who he is and why his message has resonated with young people," Newsom said after speech.

Ryan Sabouni, a Berkeley freshman, came to hear from a candidate who he thought might be on the ballot when he votes for president for the first time in 2016. Sabouni said he was open to Paul's message of curbing surveillance practices but said the Republican Party would have to shift on social issues in the future. "Their standards are going out of style," he said.

"That's where Rand Paul comes in," chimed in Daniel Caveney, a fellow freshman.

Paul, perhaps more than any other expected 2016 Republican presidential candidate, has focused on appealing to younger voters. He combines a folksy and casual style, libertarian views, and sharp accusations against the NSA to make his case.

His stop in liberal Berkeley is just one in a string he has planned to expand his and the Republican brand into traditionally hostile political territory. Asked during the event if that is the groundwork for a 2016 presidential run, Paul replied with a single word.

"Maybe."

Still, when he seeks out younger voters, Paul does not typically focus on social issues, such as gay marriage, that divide him, and his party's platform, from the views of many younger voters.

"He's obviously not going to talk about his positions on gay marriage and abortion," said Reich, now a Berkeley professor, who said that many students presume Paul to be more socially liberal than he is. "He's going to ride the coattails of that assumption—which is totally erroneous."

Paul said after the event that he didn't sidestep social issues as much as focus on the more pressing current topic of overreaching spy agencies. "I don't think it was necessarily an avoidance," he said.