The Greenland ice sheet (GrIS) is an important component of the climate system and is a key contributor to future sea level rise, as it is storing frozen water that would raise sea levels by 7.4 m should it all melt (Bamber et al., 2018). Of particular concern is the amount of global warming we are facing now and in the future, as it is becoming more likely that even if our emissions are significantly reduced, global warming will reach at least 2∘𝐶 (Arias et al., 2021). Much research concerns the future contribution of the GrIS to sea level rise for high emissions scenarios and low emission scenarios, but there are few studies giving the main focus to what is becoming a more likely future, the moderate emissions scenarios. This research aims to quantify the mass loss of the Greenland ice sheet and subsequent contribution to future sea level rise under a moderate CO2 concentration scenario over a multimillennia timescale. An idealised simulation of 3000 years, where CO2 concentrations are increased by 1% annually until reaching two times pre-industrial values and then kept constant, is run with the high-resolution Community Earth System Model version 2.1 (CESM2.1) and Community Ice Sheet Model version 2.1 (CISM2.1). The climate, run with CESM2.1, is simulated for 1000 years. After 500 years, it is assumed that the climate is close to equilibrium, and thus one climate year is used for five years of forcing the ice sheet in CISM2.1, resulting in 3000 years of ice sheet simulation. At the end of the simulation, the global mean annual temperature has increased by 5∘𝐶 and the temperature over Greenland is 9∘𝐶 warmer than pre-industrial. The rate of sea level contribution in the first centuries is lower than the observed contemporary mass loss of 0.7 mm/yr (Shepherd et al., 2020) but increases after year 710 to a rate of 1 mm/yr. Another increase in mass loss is happening from the year 1380 until the end of the simulation where the rate is 2 mm/yr and the total contribution to sea level rise is 4.1 m. The limited mass loss in the period between years 71-400 and its increase thereafter is found to relate to temporal strong weakening and posterior recovery of the NAMOC. This study projects that the GrIS is a major contributor to future sea level rise, even in a moderate warming scenario, and that the changing NAMOC has a noteworthy effect on the GrIS mass budget.