Matt Korade

(CNN) -- Rep. Cedric Richmond apologized to White House adviser Kellyanne Conway on Sunday night for making crude remarks at a Washington dinner last week about a photo showing Conway on her knees on an Oval Office sofa.

"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.