You sure about that? I'm not.
Thought experiment:
1) Put an ice cube in a glass.
2) Add just enough water so it floats. Mark the water line.
3) Archimedes principle means the cube has exactly displaced its own mass of water.
4) The void left by the melted solid ice will be exactly filled by the mass of ice from melted below the water line plus that previously floating above the water line.
5) Net result: no change
Now, for sea ice this is complicated by the fact that sea ice contains much less salt than ocean water, and also contains air bubbles, plus the effect of net adding fresh water to the surface on circulation of the ocean. I'm not sure what the net result is, but it's not obvious to me which way from zero it is.
[added from a reputable source - it appears there would be a slight rise due to the density difference
https://nsidc.org/news-analyses/news-stories/melting-floating-ice-will-raise-sea-level ]