West appeared on Wednesday's edition of the program more than a week after Kimmel mocked the musician in a viral video.
The hip-hop star retaliated with a Twitter rant after Kimmel poked fun at West's self-aggrandizing September interview with the BBC.
West told the British broadcaster he was the biggest rock star on the planet and also listed his other accomplishments.
Kimmel joked about West's lack of humility and played on "Live!" a video showing two children acting out the transcript of the BBC interview to hilarious effect.
However, West apparently didn't think the skit was funny, and took to Twitter to post messages such as: "JIMMY KIMMEL PUT YOURSELF IN MY SHOES ... OH NO THAT MEANS YOU WOULD HAVE GOTTEN TOO MUCH GOOD [expletive] IN YOUR LIFE..."
Kimmel said early in Wednesday's interview with West: "I really felt bad about all this stuff. I did," to which West replied, "M-huh."
Kimmel went on to say he knows West personally, always regarded him as friendly and thinks he is misunderstood.
"I don't know if you know this, but a lot of people think you're a jerk," Kimmel told West after the hip-hop artist declared himself an "artistic genius" and dismissed the notion he is "just a celebrity."
"I'm not running for office," West said. "I'm just here to make good music. When I did that [BBC] interview, I was really vocal with a lot of things I've been dealing over the last 10 years. For me, I'm a creative genius, and I know you're not supposed to say that about yourself. I say things the wrong way a lot of times, but my intention's always positive. For me to say I wasn't a genius, I would be lying to you and myself. "
"When you said you think you're a genius, I think that upsets people," Kimmel said. "But the truth is a lot of people think they're geniuses, but nobody says it because it's weird to say it. But it is most certainly more honest to say, 'I am a genius.'"
West told Kimmel he is often irked by his portrayal in the media as a hot-head with an inflated ego and insisted he generally keeps his frustration to himself. However, this time he said he felt he could address the issue since he knows Kimmel.
"That elevates sometimes," West said. "Jimmy does his thing. I do my thing. And, at some point, egos can flare up, and we kind of took it back to high school."
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