The Paris Agreement aims to limit global mean warming in the twenty-first century to less than 2 degrees Celsius above preindustrial levels, and to promote further efforts to limit warming to 1.5 degrees Celsius1. The amount of greenhouse gas emissions in coming decades will be consequential for global mean sea level (GMSL) on century and longer timescales through a combination of ocean thermal expansion and loss of land ice2. The Antarctic Ice Sheet (AIS) is Earth's largest land ice reservoir (equivalent to 57.9 metres of GMSL)3, and its ice loss is accelerating4. Extensive regions of the AIS are grounded below sea level and susceptible to dynamical instabilities5-8 that are capable of producing very rapid retreat8. Yet the potential for the implementation of the Paris Agreement temperature targets to slow or stop the onset of these instabilities has not been directly tested with physics-based models. Here we use an observationally calibrated ice sheet-shelf model to show that with global warming limited to 2 degrees Celsius or less, Antarctic ice loss will continue at a pace similar to today's throughout the twenty-first century. However, scenarios more consistent with current policies (allowing 3 degrees Celsius of warming) give an abrupt jump in the pace of Antarctic ice loss after around 2060, contributing about 0.5 centimetres GMSL rise per year by 2100-an order of magnitude faster than today4. More fossil-fuel-intensive scenarios9 result in even greater acceleration. Ice-sheet retreat initiated by the thinning and loss of buttressing ice shelves continues for centuries, regardless of bedrock and sea-level feedback mechanisms10-12 or geoengineered carbon dioxide reduction. These results demonstrate the possibility that rapid and unstoppable sea-level rise from Antarctica will be triggered if Paris Agreement targets are exceeded.