Icebergs have a potential impact on climate since they release freshwater over a widespread area and cool the ocean due to the take-up of latent heat. Yet, so far, icebergs have never been modelled using an ice-sheet model coupled to a global climate model. Thus, in climate models their impact on climate has been restricted to the ocean. In this study, we investigate the effect of icebergs on the climate of the mid- to high latitudes and the Greenland ice sheet itself within a fully coupled ice-sheet (GRenoble model for Ice Shelves and Land Ice, or GRISLI)-earth-system (iLOVECLIM) model set-up under pre-industrial climate conditions. This set-up enables us to dynamically compute the calving sites as well as the ice discharge and to close the water cycle between the climate and the cryosphere model components. Further, we analyse the different impact of moving icebergs compared to releasing the ice discharge at the calving sites directly. We performed a suite of sensitivity experiments to investigate the individual role of the different factors that influence the impact of the ice release on the ocean: release of ice discharge as icebergs versus as freshwater fluxes, and freshening and latent heat effects. We find that icebergs enhance the sea-ice thickness around Greenland, thereby cooling the atmosphere and increasing the Greenland ice sheet's height. Melting the ice discharge directly at the calving sites, thereby cooling and freshening the ocean locally, results in a similar ice-sheet configuration and climate as the simulation where icebergs are explicitly modelled. Yet, the simulation where the ice discharge is released into the ocean at the calving sites while taking up the latent heat homogeneously underestimates the cooling effect close to the ice-sheet margin and overestimates it further away, thereby causing a reduced ice-sheet thickness in southern Greenland. We conclude that in our fully coupled atmosphere-ocean-cryosphere model set-up the spatial distribution of the take-up of latent heat related to iceberg melting has a bigger impact on the climate than the input of the iceberg's meltwater. Moreover, we find that icebergs affect the ice sheet's geometry even under pre-industrial equilibrium conditions due to their enhancing effect on sea ice, which causes a colder prevailing climate.