You can conduct an experiment about this as well. So take a glass of water and add ice-cubes to it. Take note of the amount of water, let the ice melt. The ice that was floating above might seem like, it would increase the water level, but it stays the same. Then another way to think about it is if you freeze a glass of water it would expand, not if it melts the about of water remains the same.

Though melting of icebergs does not cause sea levels to rise, it disrupt the ocean circulation system, and causes many side effects.

(I meant interrupted, not erupted/irrupted :') )