U.S. Rep. Liz Cheney said Sunday she found the sexual misconduct allegations against fellow Republican U.S. Rep. Matt Gaetz "sickening" -- but declined to comment further against one of her most staunch critics amid an ongoing investigation.

During an appearance Sunday on CBS News' "Face the Nation," Cheney, who represents Wyoming and was the most high-profile House Republican to vote to impeach former President Donald Trump, was asked by host Margaret Brennan whether she would call for Gaetz’s resignation for allegedly violating sex trafficking laws among other allegations of misconduct. 

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"As the mother of daughters, the charges are sickening," Cheney said. "And as the speaker noted, there is an ethics investigations underway. There are also criminal investigations underway. And I'm not going to comment further on that publicly right now."

Earlier in the program, House Speaker Nancy Pelosi said it was up to the Republicans, namely House Minority Leader Kevin McCarthy, to take responsibility for investigating Gaetz’s behavior.

"Were you surprised at these allegations?" Brennan pressed Cheney.

"I’m not going to comment further," the congresswoman insisted, to which Brennan added, "He is one of your chief critics, so I needed to offer you that opportunity."

Gaetz, a Republican representing Florida who had pushed Trump’s "America First" message of limiting the use of American troops in international conflicts, repeatedly has taken aim at Cheney for following in the footsteps of her father – former Vice President Dick Cheney – in advocating for a hawkish and muscular U.S. role overseas. 

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Cheney was one of only 10 Republicans who joined all 222 House Democrats in voting to impeach Trump for inciting the Jan. 6 insurrection at the U.S. Capitol.

On Sunday, she rejected Pelosi’s notion that "we're in a good place" and said it was the House Speaker’s responsibility to create a bipartisan 9/11 style commission to investigate what the provocation was on Jan. 6 and "make sure it doesn't happen again."

"We’re not in a good place," Cheney said. "The version she put forward was not bipartisan. It was very heavily partisan toward the Democrats, and it’s a serious issue. It shouldn’t be a partisan issue. We just had 140 national security officials from Republican and Democratic administrations send a letter to Congress that we need a commission. I think that’s the single-most most important thing to do is make sure that kind of attack never happens again."

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Brennan also asked Cheney to react to Trump’s reported bombastic language at GOP fundraiser hosted at Mar-a-Lago on Saturday, to which Cheney said the former president, "used the same language he knows provoked violence on Jan. 6."

"As Republicans, we need to be focused on embracing the Constitution, not embracing insurrection," Cheney said.

Fox News' Paul Steinhauser contributed to this report.