Hmm.. AHA!!!
True20. It's a nice system with only 3 classes - basically warrior, skills, mage. The system does not go in depth on strategy, but is quite quick and fast. Abilities to do with magic are not particularly culture specific - you could have a mage with the "Summoning" talents for a demon/ghost summoner or a demon binder just as easily as say, a fireball throwing mage. Expect combats to be short and brutal, as with lethal weapons it can very quickly work out that someone gets incapacitated and then they get dead in a short period of time.
Its worth a look if you can pick it up on the cheap. The expansions really make it a fine game. I've run epic fantasy (Planescape), Western and sci fi with it equally easily. An eastern orientation wouldn't stretch the system at all.
If you want a more focused personal combat system, Riddle of Steel can't be beat. It doesn't have the Katana stuff in the original book, and it also is no longer published as far as I am aware, but were I wanting to do a duelling sword schools style game I would run Riddle of Steel. Avoid the magic in the book like the plague.
If you want a more 'feuding kingdoms' feel, I think Game of Thrones may assist you. No magic in that either, and you'd need to re-name weapons and things (Hey, a Katana is not a lot different to a sword with an extended hilt after all) but it has land, power, politics, fighting sort of stuff.
Overall I'd suggest a look at True 20. It's not particularly complex, is very granular (Stuff can be added/changed quite easily, the system is basically meant to be that way.)