Do melting icebergs contribute to sea-level rise?

When Ice on land melts, it does contribute to sea level rise. When ice slides off land into the water it causes sea level rise. To a first approximation, ice floating in water does not produce sea level rise when it melts because the water produced has the exact same volume as the water it displaced as ice. You raise an interesting question, since sea water has salt in it, it is slightly more dense than fresh water. When the ice melts, it releases fresh water, which is less dense than the salt water. So it will float on top of the salt water, and very slightly raise the local sea surface. Over time it will spread out and mix and that effect will disappear. I can't say how fast that would happen, probably depends on currents and waves and maybe other things.