In a recent interview, the guitarist maintained that he was "not advocating violence" but added that "somebody should shoot Simon Cowell" because of his influence on the music business.
"I read Martin gore wants to shoot me," Cowell said on Twitter.
"He was is in depeche mode. Do you realise how weird and stupid that makes you. Go and watch the news."
He added: "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 been criticised for several years for the effect of his talent shows on music, with The Enemy recently calling him "a parasite off people who've had bad lives".