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The response of the North Atlantic dynamic sea surface height (SSH) and ocean circulation to Greenland Ice Sheet (GrIS) meltwater fluxes is investigated using a high-resolution model. The model is forced with either present-day-like or projected warmer climate conditions. In general, the impact of meltwater on the North Atlantic SSH and ocean circulation depends on the surface climate. In the two major regions of deep water formation, the Labrador Sea and the Nordic Seas, the basin-mean SSH increases with the increase of the GrIS meltwater flux. This SSH increase correlates with the decline of the Atlantic meridional overturning circulation (AMOC). However, while in the Labrador Sea the warming forcing and GrIS meltwater input lead to sea level rise, in the Nordic Seas these two forcings have an opposite influence on the convective mixing and basin-mean SSH (relative to the global mean). The warming leads to less sea-ice cover in the Nordic Seas, which favours stronger surface heat loss and deep mixing, lowering the SSH and generally increasing the transport of the East Greenland Current. In the Labrador Sea, the increased SSH and weaker deep convection are reflected in the decreased transport of the Labrador Current (LC), which closes the subpolar gyre in the west. Among the two major components of the LC transport, the thermohaline and bottom transports, the former is less sensitive to the GrIS meltwater fluxes under the warmer climate. The SSH difference across the LC, which is a component of the bottom velocity, correlates with the long-term mean AMOC rate.