Decreasing sea ice cover and warming sea surface temperatures (SSTs) impact polar climate in uncertain ways. We aim to reduce the uncertainty by comparing output from four 41-year simulations with four Atmospheric General Circulation Models (AGCMs). In our baseline simulations, the models use identical prescribed SSTs and sea ice cover conditions representative of 1950–1969. In three sensitivity experiments, the SSTs and sea ice cover are individually and simultaneously changed to conditions representative of 2080–2099 in a strong warming scenario. Overall, the models agree that warmer SSTs have a widespread impact on 2 m temperature and precipitation while decreasing sea ice cover mainly causes a local response (i.e. largest effect where the sea ice perturbation occurs). Thus, decreasing sea ice cover causes a larger change in precipitation and temperature than warmer SSTs in areas where sea ice cover is reduced while warmer SSTs dominate the response elsewhere. In general, the response in temperature and precipitation to simultaneous changes in SSTs and sea ice cover is approximately equal to the sum due to individual changes, except in areas of sea ice decrease where the joint effect is smaller than the sum of the individual effects. The models agree less well on the magnitude and spatial distribution of the response in mean sea level pressure, i.e. uncertainties associated with atmospheric circulation responses are larger than uncertainties associated with thermodynamic responses. Furthermore, the circulation response to decreasing sea ice cover is sometimes significantly enhanced but sometimes counteracted by the response to warmer SSTs.