Anthropogenic warming has led to an unprecedented year-round reduction in Arctic sea ice extent. This has far-reaching consequences for indigenous and local communities, polar ecosystems, and global climate, motivating the need for accurate seasonal sea ice forecasts. While physics-based dynamical models can successfully forecast sea ice concentration several weeks ahead, they struggle to outperform simple statistical benchmarks at longer lead times. We present a probabilistic, deep learning sea ice forecasting system, IceNet. The system has been trained on climate simulations and observational data to forecast the next 6 months of monthly-averaged sea ice concentration maps. We show that IceNet advances the range of accurate sea ice forecasts, outperforming a state-of-the-art dynamical model in seasonal forecasts of summer sea ice, particularly for extreme sea ice events. This step-change in sea ice forecasting ability brings us closer to conservation tools that mitigate risks associated with rapid sea ice loss.