The long-term response of Greenland to anthropogenic warming is of critical interest for the magnitude of the sea-level rise and for climate-related concerns. To explore its evolution over several millennia we use a climate-ice sheet model forced by a range of CO2 emission scenarios, accounting for the natural removal of anthropogenic CO2 from the atmosphere. Above 3000 GtC, the melting appears irreversible, while below 2500 GtC, Greenland only experiences a partial melting followed by a re-growth phase. Delaying emissions through sequestration slows significantly the melting, but has only a limited impact on the ultimate fate of Greenland. Its behavior is therefore mostly dependent on the cumulative CO2 emissions. This study demonstrates that the fossil fuel emissions of the next century will have dramatic consequences on sea-level rise for several millennia.