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.