They tried once to invade Japan with a huge invasion force . A small amount of them reached land where the Japanese quickly destroyed them ! While the main force fleet was on it's way , a Typhoon blew up and the huge winds destroyed the Mongol fleet ! The Japanese called this the " Divine Wind " and believed their Gods did it . The Mongols tried one more time but only half hearted and the seas and wind knocked them out again ! Thus the Japanese phrase Divine Wind or as we know it , Kamikaze .
To the best of my knowledge they never invaded Japan. They were renowned horsemen, not seafarers. They routinely raided and sacked villages throughout the Asian mainland. They were the reason China built the Great Wall. I don't believe they ever sailed to the islands of Japan.