The 51-year-old guitarist made a flippant comment during an interview last week, in which he voiced his opinion that Simon and his talent show 'The X Factor' are not good for the music industry, and joked someone should take a gun to Simon.
Martin told Music Week: ''I'm not advocating violence, but I think somebody should shoot Simon Cowell.
''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 Simon has not taken the remark lightly after having received death threats in the past during his time as a judge on the UK version of the pop star search series.
The 52-year-old star took to his twitter account to blast Martin, angrily posting: ''I read Martin Gore wants to shoot me. Do you realise how weird and stupid that makes you? Go and 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.''
Simon's Holland Park home in west London is wired up with security worth £100,000 after his stalker Leanne Zaloumis broke in earlier this year, hiding in a wardrobe.
He previously spoke about his fears for his personal safety, saying: ''People want to kill me. It's serious and we have a lot of security now for that reason.
''My bosses told me they have been shown emails threatening my life. They said one man wanted to stab me.''