Cowell, 53, vented his fury and branded Gore a "weirdo".
In a magazine interview, guitarist Gore reportedly said: "I'm not advocating violence but I think somebody should shoot Simon Cowell.
"His influence on the industry over the last God knows how many years ... It's just like, so many people think that's what music is. What happened to bands getting together?"
Cowell tweeted: "I read Martin Gore wants to shoot me. He was in Depeche Mode. Do you realise how weird and stupid that makes you? Watch the news.
"Why I am angry about weirdo Gore is a ton of people have got shot this year and people like weirdo Gore encourage this."
Cowell has previously spoken of getting death threats and having to beef up security at his Los Angeles mansion.