Sen. Rand Paul, R-Ky., told Fox News Thursday he was "disappointed" that Chief Justice John Roberts did not read his question at the Senate impeachment trial of President Trump, saying he "did not identify anyone as a whistleblower or refer to anyone as a whistleblower."

"My question did discuss two Obama partisans who worked in the National Security Council," Paul said on "The Story with Martha MacCallum." "One of them now works for Adam Schiff, and one of them is someone who is involved in the origins of the impeachment inquiry."

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Roberts shut down a question earlier Thursday from Paul that mentioned the name of a person reported to be the Ukraine phone call whistleblower, prompting Paul to storm out of the Senate chamber and hold an impromptu press conference to read the question anyway. Fox News has not confirmed the name of the whistleblower.

Roberts, who is presiding over the trial, similarly rebuffed Paul a day earlier.

Paul wanted to ask whether Schiff and Trump's defense team were aware that a committee staff member had a close relationship with the reported whistleblower while they were on the National Security Council together.

The senator said he supported whistleblowers but argued that the statute only protects the whistleblower from being fired or other retaliation and does not keep his identity anonymous.

"If this was a concocted plot to bring down the president, that's not something the whistleblower statute was about," Paul said. "But also the whistleblower statute doesn't guarantee that you're anonymous. It guarantees that you're not fired."

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Paul also called Democrats "hypocritical" in their push to impeach Trump.

"The great irony of this entire impeachment hearing now is they're using government to go after their political opponents," Paul said. "They're mad that they say that President Trump did it and they're doing exactly the same thing in a very partisan way, which every one of them said during the Clinton impeachment was a problem."

Fox News' Gregg Re contributed to this report.