Washington (CNN) Republican Sen. Rand Paul, before a raucous crowd on Monday, demanded members of the media print the identity of the anonymous whistleblower at the heart of the House impeachment inquiry into President Donald Trump's dealings with Ukraine.

"I say to tonight to the media: do your job and print his name," Paul, a Kentucky Republican, yelled during a rally Trump held in support of Republican Gov. Matt Bevin ahead of Tuesday's gubernatorial election. The crowd of Trump supporters, many donning "READ THE TRANSCRIPT" shirts, erupted into applause and cheers, and some chanted "Do your job!" and pointed toward the area where members of the press gathered to cover the event.

Paul told the crowd "we also now know the name of the whistleblower," but did not provide any personal knowledge of the person's identity, before going on to echo baseless claims of wrongdoing by former Vice President Joe Biden and his son, Hunter. "The whistleblower needs to come before Congress as a material witness because he worked for Joe Biden at the same time Hunter Biden was getting money from corrupt oligarchs," Paul said. There is no evidence of wrongdoing by either Joe or Hunter Biden.

Several other Republicans have called for the whistleblower's identity to be revealed -- despite federal laws to protect individuals who file complaints -- but the sitting senator's insistence before a chanting crowd stands as one of the most forceful public calls yet. His comments drew swift condemnation from Democrats, who argue the person's identity has no bearing on the allegations lodged against the President.

During the rally on Monday, Paul called on Republican lawmakers to "step up" and subpoena the whistleblower, though a number of the witnesses called before House committees have corroborated what was written in the complaint about Trump's July 25 phone call with Ukrainian President Volodymyr Zelensky.

The anonymous whistleblower's complaint alleges that Trump pressured Zelensky to help his reelection by investigating Biden, as well as a White House cover-up designed to keep information about the effort, led in part by Trump's personal lawyer Rudy Giuliani, out of public view.

On Sunday, Mark Zaid, an attorney for the whistleblower, said in a series of tweets that Republicans on the House Intelligence Committee have sought to "expose our client's identity which could jeopardize their safety, as well as that of their family."

Zaid, who had been working with Congress to prevent his client's identity from being revealed if they were to be interviewed by lawmakers, on Sunday offered to have Republican lawmakers submit questions to his client directly without having to go through the committee's Democratic majority.

In September, the President said in a tweet, "Like every American, I deserve to meet my accuser," and he has since continued his calls for the whistleblower to be outed as House Democrats ratchet up their impeachment inquiry and tensions over the whistleblower's identity have deepened.

Two sources previously described to CNN a pattern of GOP questioning -- over the course of several congressional depositions related to the probe -- that appeared designed to try to identify the whistleblower through the course of asking witnesses, and putting into the deposition record, the names of various government officials involved that may fit the professional description that has been made public of the individual. Democrats and Republicans got into a shouting match over the matter last week during a closed door interview with a witness.

'Deeply troubling and disappointing'

Sen. Angus King, an independent from Maine who caucuses with Democrats, on Tuesday criticized Paul, telling CNN's John Berman on "New Day" that the senator's calls are a distraction from the impeachment inquiry spurred by the whistleblower's complaint.

"I went back and read the complaint last night. Virtually everything in that complaint has now been verified in public and public testimony, particularly the transcript of the -- the partial transcript ... of the call confirms exactly what the whistleblower said. So who it is -- I don't care if it's (New England Patriots quarterback) Tom Brady, it doesn't matter because the investigation is 'what happened?' This is a distraction," King said.

"It's deeply troubling and really disappointing," he said.

Later on the same program, Rep. Jamie Raskin, a Maryland Democrat who sits on two of the House panels involved in the impeachment inquiry, said it's "very dangerous stuff to be scapegoating and targeting the whistleblower."

Raskin argued that the "attempt to demonize and vilify the whistleblower is a scapegoating tactic" that is a "distraction from the merits of the case."