Gaetz and Trump rep. Jason Miller contradicted CNN's report that Gaetz was denied a meeting with the former president.
Gaetz denied that he paid women for sex - including, potentially, an underage girl - blaming the media for what he said were "conspiracy theories."
The committee also opened a separate investigation into Rep. Tom Reed over allegations of sexual misconduct.
The nameless statement from "The Women of the Office of U.S. Congressman Matt Gaetz" said the allegations against him were false.
Reports of a sex crimes investigation morphed into an elaborate saga involving ex-government officials and a US hostage who's presumed dead.
Investigators are looking at whether women were trafficked across state and international lines during trips with Gaetz, CBS News reported.
"I'm not here to provide any degree of evidence in support of Congressman Gaetz, only to discredit these baseless allegations," Nathaniel Nelson said.