Getty Images Kellyanne Conway in the Oval Office
"I really just want to know what was going on there," Richmond said at the dinner. "Because she really looked kind of familiar there in that position there. But don't answer. And I don't want you to refer back to the '90s."
Conway previously said she was kneeling on the couch in order to take a photo of the president posing with dozens of leaders of Historically Black Colleges and Universities.
The White House demanded an apology and Republican National Chairwoman Ronna Romney McDaniel accused Richmond of sexism.
"You may think this is funny, but it's not. It's disgusting & offensive," McDaniel tweeted on Thursday. "A snarky joke for you is just a reminder of the demeaning comments women hear every single day."
It was a Republican-Sen. Tim Scott-who brought up the photo of Conway a few minutes before Richmond's comment.
"Has anyone seen the controversy around Kellyanne Conway and the couch in the Oval Office?" Scott asked the crowd of journalists and lawmakers. "Come on, people. You remember the '90s. That couch has had a whole lot of worse things. Come on now."
Richmond defended himself when asked by a reporter after the event if the joke was meant to be lewd.
"I just said she looked comfortable in that position," Richmond said. "I can't let Tim get away with making a Clinton joke without making one of my own."
In a statement on Thursday, Richmond attempted to clarify his comment, but did not apologize.
"Where I grew up saying that someone is looking or acting 'familiar' simply means that they are behaving too comfortably," Richmond said. "I decided to use that joke due to the large social media backlash over her inappropriate posture considering there were more than 60 HBCU Presidents in the room."