"I think there are reasons to have whistleblower statutes, and have anonymity. But if you're accusing somebody of something with the ramifications of impeachment, I think really the person ought to come forward," he added.

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Paul's comments come as President Trump has doubled down publicly on his demand to know the identity of the whistleblower behind the growing controversy over Trump's interactions with Ukraine. The New York Times reported last week that the individual is a male CIA agent.