Ensemble experiments with a climate model are carried out in order to explore how incorporating a stochastic ice strength parameterization to account for model uncertainty affects estimates of potential sea ice predictability on time scales from days to seasons. The impact of this new parameterization depends strongly on the spatial scale, lead time and the hemisphere being considered: Whereas the representation of model uncertainty increases the ensemble spread of Arctic sea ice thickness predictions generated by atmospheric initial perturbations up to about 4 weeks into the forecast, rather small changes are found for longer lead times as well as integrated quantities such as total sea ice area. The regions where initial condition uncertainty generates spread in sea ice thickness on subseasonal time scales (primarily along the ice edge) differ from that of the stochastic sea ice strength parameterization (along the coast lines and in the interior of the Arctic). For the Antarctic the influence of the stochastic sea ice strength parameterization is much weaker due to the predominance of thinner first year ice. These results suggest that sea ice data assimilation and prediction on subseasonal time scales could benefit from taking model uncertainty into account, especially in the Arctic.