Rapid and extensive growth of sea ice cover was suggested to play a major role in the sea ice switch mechanism for the glacial cycles as well as on shorter millennial scales [Gildor and Tziperman, 2000]. This mechanism also predicts a hysteresis between sea ice and land ice, such that land ice grows when sea ice cover is small and withdraws when sea ice cover is more extensive. The switch‐like sea ice growth and the hysteresis were previously demonstrated using a simple, highly idealized box model. In this work we demonstrate a switch‐like sea ice behavior as well as the sea ice–land ice hysteresis using a coupled climate model that is continuous in the latitudinal dimension. It is shown that the switch‐like sea ice growth occurs when the initial meridional atmospheric temperature gradient is not too strong. It is also shown that the meridional extent to which sea ice grows in a switch‐like manner is not affected by the intensity of the thermohaline circulation, which does, however, influence the climate cooling that is needed to trigger such rapid sea ice growth.