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?
Girls probably love this. I have been in this situation and the guy didn't realize that we had a number of mutual friends. The best thing to do is to take the high road and ignore it. Tell her about it and see what she says. If she still shows any loyalty to the old boyfriend then you probably don't want to date her regardless of who can or does kick who's ass. Also if she *wants* you to kick his ass, then that's not really great either.