House Republican leaders, in a fiery news conference Tuesday, said House Intelligence Committee Chairman Rep. Adam Schiff, D-Calif., prevented a witness in the latest impeachment hearing from answering certain questions from Republican members.

Rep. Steve Scalise, R-La., and Rep. Jim Jordan, R-Ohio, told reporters that Schiff shut down a Republican line of questioning during a hearing with Army Lt. Col. Alexander Vindman, the latest current or former Trump administration official to come before Congress in relation to the impeachment probe.

"When we asked [Vindman] who he spoke to after important events in July -- Adam Schiff says, 'no, no, no, we're not going to let him answer that question,"' Jordan said.

Jordan went on to say that Schiff seemed to be breaking his own rules for the hearings, implying the chairman was acting almost as a "lawyer" for Vindman.

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Vindman, who serves as a director on the National Security Council (NSC), arrived Tuesday morning to testify before the House Intelligence, Oversight, and Foreign Affairs committees. He expressed concern in his prepared opening statement, obtained by Fox News, over Trump's request to have Ukraine investigate political opponents.

It also states that he does not know who the whistleblower is whose complaint spurred the beginning of the Democrats' current impeachment inquiry and does not feel comfortable speculating about the whistleblower's identity. The inquiry was opened after a whistleblower complaint alleged that Trump, during the July phone call, pushed Zelensky to investigate former Vice President Joe Biden and his son Hunter as military aid to the country was being withheld.

"The Democrats run out here and say, 'ooh, the Republicans are trying to figure out who the whistleblower is,'" Jordan continued. "We're trying to figure out who our witness list is! The resolution that the Speaker has just filed ... she points this out in the resolution that this is going to go to the Judiciary Committee if in fact they push it there. There will be witnesses called. We would like to figure out who those witnesses should be."

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"I pointed out last week there 435 members of Congress ... only one of them knows who the whistleblower is, more importantly, who the sources are for the whistleblower who were the basis of him filing this complaint. Now he doesn't want anyone else to know that," Jordan said.

Scalise then proceeded to attack the impeachment proceedings in general, using the latest GOP procedural complaint in a further attempt to discredit the Democrats' impeachment push.

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"It's clear Pelosi needs to declare a mistrial," Scalise said. "This has been a tainted process from the start. What happened today confirms even worse just how poorly Adam Schiff is handling this process, denying the ability for Republicans to even ask basic questions that are critical to the heart of whether or not a President of the United States is impeached."

Fox News' Ronn Blitzer and Frank Miles contributed to this report.