"Despicable. I hope @KellyannePolls receives the apology she deserves-certainly never thought I'd write that & I mean every word," Clinton wrote.
The former first daughter's tweet was in response to an attempted joke made Wednesday night by Democratic Congressman Cedric Richmond, who in January was tapped to lead the Congressional Black Caucus.
Conway, who serves as White House counselor to President Donald Trump, wrote back, thanking Clinton for her support and praising her as a fellow "strong" woman.
"Thank you, @ChelseaClinton. As strong women, as moms to Charlottes...appreciate you speaking out on this," she tweeted later in the day. (Both women have daughters named Charlotte.)
Richmond made the comment, which referenced a now-viral photo of Conway on a couch in the Oval Office, at the Washington Press Club Foundation's annual dinner Wednesday night.
The dinner, attended by journalists and politicians alike, featured standup routines from Richmond, as well as Republican Sen. Tim Scott. Scott spoke first, and made a joke that "a whole lot worse" had happened on the couch, an apparent reference to the Monica Lewinsky scandal.
In an effort to one-up his Republican counterpart, Richmond also referenced the photo, saying Conway "looked familiar" in the position. Both attempts at humor largely fell flat.
The WCPF's mission is "to promote equality, education and excellence among journalists in print and broadcast media," per its website
, and it was originally founded in 1919 to "ensure that women established an equal place in the newsroom."
The Louisiana congressman clarified Thursday that his joke was not intended as innuendo.
"Where I grew up saying that someone is looking or acting 'familiar' simply means that they are behaving too comfortably. 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," Richmond said in the statement.
A spokesman for the congressman declined to comment to CNN on whether Richmond would apologize to Conway.
Friday's tweets come as Clinton has stepped up her social media presence in recent weeks, criticizing the Trump administration and weighing in on the news of the day with sharply worded, and sometimes sarcastic, tweets.
Clinton even sparred with Conway recently, knocking her for citing a non-existent terrorist attack to justify the administration's travel ban.
"Very grateful no one seriously hurt in the Louvre attack ...or the (completely fake) Bowling Green Massacre. Please don't make up attacks," Clinton tweeted
Conway fired back herself, writing
, "Bosnia lie a Great reminder. And 2 @ChelseaClinton & others, you can't "invent" quality candidates either. I misspoke; you lost the election."