But West ordered him to make a public apology and said Kimmel's life would be "much better" if he did so, Kimmel said, adding that West also called himself the most powerful voice in media.
Then came more than a half-dozen tweets posted on West's official Twitter site. One called Kimmel out of line for spoofing what West called "the first piece of honest media in years," and another referred to photographers trying to get shots of West's baby daughter with Kim Kardashian.
"Jimmy Kimmel, I don't take it as a joke. ... You don't have scum bags hopping over fences trying to take pictures of your daughter," West tweeted. Other tweets used profanity and coarse language, while one mocked Kimmel by saying his former girlfriend Sarah Silverman is funnier than him.
"Finally, I'm in a rap feud. I always wanted to be in a rap feud," a smiling Kimmel said.
Representatives for Kimmel in Los Angeles and West in New York didn't immediately respond to requests for comment made early Friday, outside of business hours.
In a tweet Kimmel posted before the show, he said West's attack was "not a prank, I promise," unless West was playing one on him. Kimmel has done his share of high-concept comedy, including a show in which Matt Damon tied him up onstage and took over as host.
West is known for his outbursts, not his humor.
The incident capped a big week for "Jimmy Kimmel Live," with shows including Hollywood street concerts with Paul McCartney and Justin Timberlake.
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