Earlier in the day, Melania Trump, in her first speech on the 2016 trail
, said she'd work to improve a social media culture that she said has gotten "too mean and too tough" if she became first lady.
"Doesn't this start at home?" Cooper asked Conway on "Anderson Cooper 360." "Isn't the problem at her own dinner table?"
"No, it's not at her own dinner table," Conway fired back. "The fact that her husband is running for president and defends himself sometimes or tweets things out --"
"Talking about Carly Fiorina's face wasn't a counterattack. That was just an attack," Cooper interjected. He was referring to Trump's attack on the former Hewlett Packard CEO and Republican presidential hopeful in September 2015 when he said "Look at that face! Would anyone vote for that? Can you imagine that, the face of our next president?"
"I am sorry?" asked Conway.
"Talking about Carly Fiorina's face was not a counterattack or counterpunch," Cooper said. "That was just mean."
Conway responded that he had rescinded the comments "on a national stage" -- referring to a CNN Republican primary debate in California.
"He went on a national stage, in front of tens of millions of people... and said that she has a very beautiful face, that she's a beautiful woman."
Conway added that she personally was proud that Fiorina was part of the Republican Party.
She said that the media tended to "cherry pick" posts from Trump's social media presence to highlight insulting behavior.
"I know, it's full of this stuff, though," Cooper responded.