I would want you to hang around while I beat his ass myself. Then you can put ice on my sore knuckles and blot the sweat from my forehead. Maybe have a cool drink waiting.
Seriously, ignore it until it can't be ignored - then do what you have to do. Most men spout bullshit for ego's sake - and until he confronts you physically, you can't really know what he's going to do; most likely he's just blowing hot air. You would be the better man if you didn't go looking for trouble, just go on with your life.
I'm curious, does your girlfriend know what her ex is saying?