"What we don't know is was President Obama told that the evidence to get this investigation started was paid for by the Hillary Clinton campaign?" Paul said, referring to the infamous Steele dossier.

"We need to know that." Paul said, adding that communications between Obama-era officials including James Comey and John Brennan, the former respective heads of the FBI and CIA, also need to be made public so the "entire story" can be understood.

"It was so scandalous and so unverified and has turned out to be untrue, and yet this was the basis for the beginning of the investigation. This was the basis for doing something extraordinary," Paul said of the dossier.

"I think it's very important that we not turn our country into this back and forth where each successive party tries to use the apparatus of government to investigate the previous president," Paul also noted.