The Florida congressman, 38, has been accused of violating federal sex-trafficking laws, paying women for sex and showing nude photos of women he claimed to have slept with to fellow lawmakers.
Mr Gaetz is the subject of an Ethics Committee investigation and a Justice Department probe. He has denied the allegations against him and has claimed he is the subject of an extortion plot.
In a statement, the Ethics Committee said it was looking into claims Mr Gaetz may have engaged in “sexual misconduct and/or illicit drug use, shared inappropriate images or videos on the House floor, misused state identification records, converted campaign funds to personal use, and/or accepted a bribe, improper gratuity, or impermissible gift, in violation of House Rules, laws, or other standards of conduct.”
Mr Gaetz has faced calls to resign from both Democrats and members of his own party, but Ms Cheney – the third-highest ranking Republican in the House – refused to be drawn on whether Mr Gaetz should stand down during an interview with CBS’s Face the Nation on Sunday.
“You know, as the mother of daughters, the charges certainly are sickening,” Ms Cheney said of Mr Gaetz, one of her chief critics within the GOP.
“And as the speaker noted, there’s an ethics investigation underway. There are also criminal investigations underway. I’m not going to comment further on that publicly right now,” she added.
Pressed by host Margaret Brennan on whether she was surprised when the allegations emerged, Ms Cheney responded: “I’m not going to comment further, Margaret.”
Trump-ally Mr Gaetz has remained defiant in the face of the allegations, telling a crowd at the Save America Summit that he was the victim of wild conspiracy theories.
“I have not yet begun to fight for the country I love and the nation I know benefits from America first principles,” he said.
“I’m built for the battle, and I’m not going anywhere.”