Net Arctic Ocean primary production (PP) is expected to increase over this century, due to less perennial sea ice and more available light, but could decrease depending on changes in nitrate (NO3) supply. Here Coupled Model Intercomparison Project Phase 5 simulations performed with 11 Earth System Models are analyzed in terms of PP, surface NO3, and sea ice coverage over 1900–2100. Whereas the mean model simulates reasonably well Arctic-integrated PP (511 TgC/yr, 1998–2005) and projects a mild 58 TgC/yr increase by 2080–2099 for the strongest climate change scenario, models do not agree on the sign of future PP change. However, similar mechanisms operate in all models. The perennial ice loss-driven increase in PP is in most models NO3-limited. The Arctic surface NO3 is decreasing over the 21st century (−2.3 ± 1 mmol/m3), associated with shoaling mixed layer and with decreasing NO3 in the nearby North Atlantic and Pacific waters. However, the intermodel spread in the degree of NO3 limitation is initially high, resulting from >1000 year spin-up simulations. This initial NO3 spread, combined with the trend, causes a large variation in the timing of oligotrophy onset—which directly controls the sign of future PP change. Virtually all models agree in the open ocean zones on more spatially integrated PP and less PP per unit area. The source of model uncertainty is located in the sea ice zone, where a subtle balance between light and nutrient limitations determines the PP change. Hence, it is argued that reducing uncertainty on present Arctic NO3 in the sea ice zone would render Arctic PP projections much more consistent.