"After a discussion with people I know and trust, I understand the way my remarks have been received by many," the Louisiana Democrat said in a statement. "I have consistently been a champion for women and women's issues, and because of that the last thing I would want to ever do is utter words that would hurt or demean them. I apologize to Kellyanne Conway and everyone who has found my comments to be offensive."
Richmond joked about the viral photo at the Washington Press Club Foundation's congressional dinner by alluding to President Bill Clinton's extramarital affair with Monica Lewinsky in the Oval Office.
"I really just want to know what was going on there, because, you know, I won't tell anybody," Richmond said. "And you can just explain to me that circumstance -- because she really looked kind of familiar in that position there. Don't answer -- and I don't want you to refer back to the 1990s."
In a tweet shortly after, Republican National Committee Chairwoman Ronna Romney McDaniel called
Richmond's attempted joke "disgusting" and "offensive."
Chelsea Clinton also tweeted out criticisms of his remarks, calling them "despicable" and saying he should apologize to Conway.
The dinner, attended by journalists and politicians alike, featured standup routines from Richmond and Republican Sen. Tim Scott of South Carolina. Scott, who spoke first, made a joke that "a whole lot worse" had happened on the couch.
Richmond's statement Sunday characterized his remarks as "an effort to one-up" the Republican senator.
In an interview with CNN's "State of the Union" Sunday, anchor Jake Tapper asked House minority leader Nancy Pelosi about whether Richmond should apologize to Conway. But the California Democrat declined to criticize Richmond, saying she wasn't aware of the video, despite widespread coverage in recent days.
She then pivoted to discussing a 2005 "Access Hollywood" tape in which Trump bragged about sexually assaulting women by grabbing their genitals without permission.
"You all are criticizing Cedric for something he said in the course of the evening, and he maybe should be criticized for that; I just don't know the particulars," Pelosi said. "But I do, every day, marvel at the fact that somebody who said the gross and crude things that President Trump said -- he wouldn't even be allowed in a frat house, and he's in the White House."
Pelosi also suggested that Richmond's remark fit within the context of the evening, but said she wasn't there to hear it.
"I think everybody was making crude comments," she said. "And I just -- I just don't know. I wasn't at that dinner."