"The reaction from a number of people, mostly her critics, is that her husband is part of the problem," Cooper asked Trump's campaign manager on "Anderson Cooper 360." "If it's not okay for kids to do this, why is it okay for adults? For Donald Trump?"
"Well, it's really not okay for anyone to do it with malicious intent," Conway said. "But I hate to break it to the political class or even the media, but most of what's on Twitter is not about politics or journalism."
She said that Melania Trump had been discussing a "cultural fact," rather than one of political relevance.
"But your candidate is the guy on Twitter at 3 a.m. tweeting out this stuff," Cooper said. "Talking about, I mean, Carly Fiorina's face."
"Do you see what's written about you or me routinely?" Conway responded. "We have to have really broad shoulders."
She tried to pivot, praising Melania Trump for her commitment to "do something about the negativity" on social media as first lady, but Cooper continued to press her.
"The question is, doesn't this start at home?" he asked. "Isn't the problem at her own dinner table?"
"No," Conway said. "The fact that her husband is running for president and defends himself sometimes or tweets things out?"
"Talking about Carly Fiorina's face, that wasn't a counterattack," Cooper said, citing Trump's comment about his former Republican primary rival in a September 2015 interview with Rolling Stone.
"Look at that face!" Trump said, according to the interview. "Would anyone vote for that?"
"That was just an attack," Cooper said. "That was just mean."
"And he went on the national stage in front of tens of millions of people, I would presume, and said that she has a very beautiful face," Conway responded.
She told Cooper to look at Trump's "message," rather than "cherry-picking" individual posts and comments.
"Go look at his entire Twitter feed," Conway said.
"It's full of this stuff, though," Cooper said.
Conway responded with an awkward laugh. "It's full of a lot of things," she said.
Watch part of the exchange below: