Adding melting water to water lowers the water level, because water is less dense than ice.
I remember getting that very question at university, and the whole class failed that question.
We assume that if the ice melts, it adds to the overall level of the water; however, physically, it does not.
Because ice is denser than water, it raises the level due to the water it displaces so that it may float - once the ice melts, it is at the same density, so the water level goes back to its original level.
I'm sure somebody smarter than me can explain it more eloquently.