Abstract. Ice loss from the Antarctic ice sheet (AIS) is expected to become the major contributor to sea-level rise in the next centuries. Projections of the AIS response to climate change based on numerical ice-sheet models remain challenging to establish due to the complexity of physical processes involved in ice-sheet dynamics, including instability mechanisms that can destabilise marine sectors with retrograde slopes. Moreover, uncertainties in ice-sheet models limit the ability to provide accurate sea-level rise projections. Here, we apply probabilistic methods to a hybrid ice-sheet model to investigate the influence of several sources of uncertainty, namely sources of uncertainty in atmospheric forcing, basal sliding, grounding-line flux parameterisation, calving, sub-shelf melting, ice-shelf rheology and bedrock relaxation, on the continental response of the Antarctic ice sheet to climate change over the next millennium. We provide probabilistic projections of sea-level rise and grounding-line retreat and we carry out stochastic sensitivity analyses to determine the most influential sources of uncertainty. We find that all sources of uncertainty, except perhaps the bedrock relaxation times, contribute to the uncertainty in the projections. We show that the sensitivity of the projections to uncertainties increases and the contribution of the uncertainty in sub-shelf melting to the uncertainty in the projections becomes more and more dominant as the scenario gets warmer. We show that the significance of the AIS contribution to sea-level rise is controlled by marine ice-sheet instability (MISI) in marine basins, with the biggest contribution stemming from the more vulnerable West Antarctic ice sheet. We find that, irrespectively of parametric uncertainty, the strongly mitigated RCP 2.6 scenario prevents the collapse of the West Antarctic ice sheet, that in both RCP 4.5 and RCP 6.0 scenarios the occurrence of MISI in marine basins is more sensitive to parametric uncertainty and that, almost irrespectively of parametric uncertainty, RCP 8.5 triggers the collapse of the West Antarctic ice sheet.