Sen. Rand Paul (R-Ky.) warned Sunday that if Edward Snowden "cozies up" to Russia, China, or governments perceived to be at odds with the United States, he will face problems.

"If he cozies up to the Russian government, the Chinese government, or any of these governments that are perceived still as enemies of ours, I think that will be a real problem for him," Paul said on CNN's "State of the Union."

But if Snowden "goes to an independent third country like Iceland and if he refuses to talk to any formal government," Paul said, there is a "chance he will be seen as an advocate of privacy."

Snowden recently revealed information about the U.S. government's sweeping surveillance efforts. He had taken refuge in Hong Kong, but reportedly left for Moscow Sunday. His final destination remains unknown.

Paul, who has been an outspoken opponent of efforts to collect Americans' phone records, said he thinks Snowden will be judged by history alongside Director of National Intelligence James Clapper, who Paul has accused of lying to Congress.

"I do think when history looks at this, they are going to contrast the behavior of James Clapper, our National Intelligence Director, with Edward Snowden. Mr. Clapper lied in Congress in defiance of the law, in the name of security. Mr. Snowden told the truth in the name of privacy," Paul said.