Japanese Horror Flick?

I watched the end of a Japanese Horror flick when I was on vacation in Jamaica about a year ago. I have no idea what the name of the movie is and would like to see the beginning of the movie. It's about a single mother and her daughter (about 8 or 9 years old) and they move into an apartment. There was a ghost of another little girl who died in a watertower so the water was infected by her. At the end the mother grabs her child and runs into the elevator but the girl isn't her daughter its the ghost child. When her real daughter opens the elevator door a large gush of water comes out and nothing else...her mother is gone. It flashes forward a couple of years and the daughter is grown and goes back to the apartment and talks with a ghost of her mother. That's all I remember. Please tell me the name of this movie!