I wanna say this was a PS1 game, but it might have been PS2. I played it back at my friend's house in like 2003, but the game was probably older. It was Japanese, I believe, and I think you were in dungeons and you fought monsters in it. I think the dungeon traversing was in first-person and I think you could summon other monsters to fight, kind of like Pokémon.
I'm not sure that narrows it down much (although my gut's saying to take a look at the SMT games, maybe Soul Hackers). Can you think of anything more unique?