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Abstract Understanding the future fate of the Greenland Ice Sheet (GIS) in the context of anthropogenic CO2 emissions is crucial to predict sea level rise. With the fully coupled Earth system model of intermediate complexity CLIMBER‐X, we study the stability of the GIS and its transient response to CO2 emissions over the next 10 Kyr. Bifurcation points exist at global temperature anomalies of 0.6 and 1.6 K relative to pre‐industrial. For system states in the vicinity of the equilibrium ice volumes corresponding to these temperature anomalies, mass loss rate and sensitivity of mass loss to cumulative CO2 emission peak. These critical ice volumes are crossed for cumulative emissions of 1,000 and 2,500 GtC, which would cause long‐term sea level rise by 1.8 and 6.9 m respectively. In summary, we find tipping of the GIS within the range of the temperature limits of the Paris agreement.