On Tuesday's show, Kimmel mocked Morrissey, saying: "While I respect his stance on this, I really do, there's a very good reason why I didn't dump the Duck Dynasty guys for Morrissey. And that's because they have guns."
He then poked fun at the singer's famously morose image, saying, "He keeps finding new ways to depress us."
On Wednesday, Morrissey issued a strongly worded statement saying he was "disappointed" in Kimmel for making jokes about depression, healthy eating and animal rights.
"Furthermore, he found time to jokingly promote gun-ownership -- hugely amusing for the parents at Sandy Hook, no doubt," he continued. "He also promoted his special guests [from] Duck Dynasty – who kill beings for fun. None of the above issues are, of course, as important as Jimmy Kimmel himself, who has finally revealed his show to have an overwhelming loss of meaning. Tune in and relive the intellectual fog of the 1950s."
Kimmel responded with a tweet: "If you have more dumb statements to make, I invite you to make them where I do, on my show."
On Wednesday's show, he again addressed the tiff in his opening monologue.
"This has nothing to do with people who eat meat versus people who don't," he said. "I’m completely respectful of people who do not eat meat, but the statement he made is ridiculous. I'd like to invite him to join the show to discuss. I'm an open, even-handed person, and I consider all points of view."
Kimmel repeated that last line several times, then quipped: "If I keep saying it, maybe it will be true. I've invited him to talk this out, and perhaps we will both be better men for it, but probably not."