Music mogul Cowell (52) erupted on Twitter after reading the comments, saying: "A ton of people have been shot this year -- and weirdos like Gore encourage it."
The bad blood between the two men stems from their very different musical backgrounds.
Gore accused Cowell, the man behind novelty music acts including the Tellytubbies and Mighty Morphin Power Rangers, of having a negative impact on the music industry.
He also said that talent shows such as The X Factor and American Idol encouraged generic and formulaic acts to flourish.
"So many people think that that's what music is," Gore said. "What happened to bands getting together? They are very few and far between now and the ones that do probably can't afford to get into a studio and make a record."
But Cowell was less than impressed with Gore's comments. "I read Martin Gore wants to shoot me," Cowell wrote on his Twitter account. "He was in Depeche Mode. Do you realise how weird and stupid that makes you. Go and watch the news."
Cowell has received several death threats since he rose to fame on Pop Idol.
Earlier this year, he was left traumatised when former beauty queen and stalker Leanne Zaloumis broke into his London home and hid in a wardrobe, after scaling a fence and smashing a window with a brick.