The impact of climate warming on the ocean near Greenland is investigated with a high resolution coupled global climate model. The ocean around Greenland exhibits a strong warming in response to a four times increase of present-day atmospheric CO2 levels. The signal is intensified in the intermediate layer and regionally strongest in the Greenland Sea. The projected changes in temperature are driven by changes affecting the large-scale ocean circulation rather than changes of the local atmospheric heat forcing. The ocean conditions examined here provide a background for the water masses in contact with the outlet glaciers around the Greenland coast. The future warming of the warm subtropical-origin layer could thus lead to enhanced ice sheet melting, although the signal could be mitigated by other effects, including an enhanced stratification of the surface fresh layer. Applying a simple parameterization to estimate the change in melt rate along the Greenland coast, we find that ice sheet melting increases everywhere in response to the change in water mass properties, although the melt rate changes show large variations in space. The largest melting acceleration is found on the east coast between Fram Strait and Denmark Strait, where both the parameterization applied to present-day conditions and observations suggest moderate melting up to now. These model results caution that the Greenland Ice Sheet mass balance should be monitored everywhere and not only where melting occurs at the moment.