Climate projections for the 21st century indicate a gradual decrease of the Atlantic Meridional Overturning Circulation (AMOC). The weakening could be accelerated substantially by meltwater input from the Greenland Ice Sheet (GIS). Here we repeat recent experiments conducted for the Intergovernmental Panel of Climate Change, providing an idealized additional source of freshwater along Greenland's coast. For conservative and high melting estimates, the AMOC reduction is 35% and 42%, respectively, compared to a weakening of 30% for the original A1B scenario. Even for the high meltwater estimate the AMOC recovers in the 22nd century. The impact of the additional fresh water is limited to further enhancing the static stability in the Irminger and Labrador Seas, whereas the backbone of the overturning is maintained by the overflows across the Greenland-Scotland Ridge. Our results suggest that abrupt climate change initiated by GIS melting is not a realistic scenario for the 21st century.