The connection to Myoho-in Temple was so close that when the Retired Emperor Goshirakawa relocated Myoho-in Temple on Mt. Hiei to Kyoto, the head priest of Myoho-in Temple would be sent to Ima Hie-jinja Shrine and Hoju-ji Temple, and there was a chance that is could be considered a Monzeki Temple (a temple traditionally served by head priest related to the Imperial family).
とくに妙法院との関係は密接で、後白河上皇が比叡山の妙法院を京都に移した際、妙法院住職に法住寺、新日吉神社を付託し門跡寺院としたという機縁がある。