That's like stating that the level of the liquid in your FULL glass of iced-water will overflow when the ice cubes floating within it melt.
If the ice-cubes are displacing a certain volume that will be replaced by the melt-water, how can the level rise?
It's mostly the expansion of the oceans' water owing to the raising of its temperature that is expected to raise sea levels and the melting of land ice (in glaciers) rather than "ice bergs".
Or am I just being a nitpicker?
(Sir) Lunchalot Physics Guru Extraordinaire
And every time a streaker ran, The stands would roar non-stop; "They must be draped," cried Hanrahan, "Or underwear will drop!"
