The two began sparring earlier this month after Morgan, an editor and columnist for the Daily Mail, battled comedian Jim Jefferies on HBO's "Real Time with Bill Maher.
"This is what you do, Piers. You say, 'He hasn't done this, he hasn't done that, he's not going to do all these things,'" Jefferies said. "Give him a f--king chance, mate. Hitler didn't kill the Jews on the first day, he worked up to it, mate."
Morgan told Carlson Monday night that he finds the comparisons of President Donald Trump to Adolf Hitler "incredibly offensive," because "it diminishes the scale and importance and horror of what Hitler did."
“Donald Trump, to my knowledge, has not murdered anybody," Morgan said. "But of course you try and say this, and if you're not prepared now in the liberal world to say that he's the new Hitler and you're not prepared to say every Muslim is banned from the country, you yourself then become the Devil and that's what happened to me.”