Does it happen at any throttle setting?
It looks like your 2002 ZX-6R is carbureted, so it could have something to do with your jets. Different components of the carburettor are responsible for different throttle settings. If its actually low throttle settings instead of low engine speeds, I'd try cleaning the carbs and adjusting the settings.

Otherwise, I'd check the battery voltage. It's possible there is a problem with your charging system, and you aren't getting enough voltage for a good spark until the engine and generator are turning at a higher speed.