Human-induced climate change could cause global sea-level rise. Through the dynamic adjustment of the sea surface in response to a possible slowdown of the Atlantic meridional overturning circulation^{1, 2}, a warming climate could also affect regional sea levels, especially in the North Atlantic region³, leading to high vulnerability for low-lying Florida and western Europe^{4, 5, 6}. Here we analyse climate projections from a set of state-of-the-art climate models for such regional changes, and find a rapid dynamical rise in sea level on the northeast coast of the United States during the twenty-first century. For New York City, the rise due to ocean circulation changes amounts to 15, 20 and 21 cm for scenarios with low, medium and high rates of emissions, respectively, at a similar magnitude to expected global thermal expansion. Analysing one of the climate models in detail, we find that a dynamic, regional rise in sea level is induced by a weakening meridional overturning circulation in the Atlantic Ocean, and superimposed on the global mean sea-level rise. We conclude that together, future changes in sea level and ocean circulation will have a greater effect on the heavily populated northeastern United States than estimated previously^{7, 8, 9}.