On the basis of projected losses of their essential sea-ice habitats, a United States Geological Survey research team concluded in 2007 that two-thirds of the world's polar bears (Ursus maritimus) could disappear by mid-century if business-as-usual greenhouse gas emissions continue1. That projection, however, did not consider the possible benefits of greenhouse gas mitigation. A key question is whether temperature increases lead to proportional losses of sea-ice habitat, or whether sea-ice cover crosses a tipping point and irreversibly collapses when temperature reaches a critical threshold. Such a tipping point would mean future greenhouse gas mitigation would confer no conservation benefits to polar bears. Here we show, using a general circulation model, that substantially more sea-ice habitat would be retained if greenhouse gas rise is mitigated. We also show, with Bayesian network model outcomes, that increased habitat retention under greenhouse gas mitigation means that polar bears could persist throughout the century in greater numbers and more areas than in the business-as-usual case. Our general circulation model outcomes did not reveal thresholds leading to irreversible loss of ice; instead, a linear relationship between global mean surface air temperature and sea-ice habitat substantiated the hypothesis that sea-ice thermodynamics can overcome albedo feedbacks proposed to cause sea-ice tipping points. Our outcomes indicate that rapid summer ice losses in models and observations represent increased volatility of a thinning sea-ice cover, rather than tipping-point behaviour. Mitigation-driven Bayesian network outcomes show that previously predicted declines in polar bear distribution and numbers are not unavoidable. Because polar bears are sentinels of the Arctic marine ecosystem, and trends in their sea-ice habitats foreshadow future global changes, mitigating greenhouse gas emissions to improve polar bear status would have conservation benefits throughout and beyond the Arctic.