Calculations were performed with the Earth system model of intermediate complexity LOVECLIM to study the response of the Greenland and Antarctic ice sheets to sustained multi-millennial greenhouse warming. Use was made of fully dynamic 3D thermomechanical ice-sheet models bidirectionally coupled to an atmosphere and an ocean model. Two 3,000-year experiments were evaluated following forcing scenarios with atmospheric CO2 concentration increased to two and four times the pre-industrial value, and held constant thereafter. In the high concentration scenario the model shows a sustained mean annual warming of up to 10°C in both polar regions. This leads to an almost complete disintegration of the Greenland ice sheet after 3,000 years, almost entirely caused by increased surface melting. Significant volume loss of the Antarctic ice sheet takes many centuries to initiate due to the thermal inertia of the Southern Ocean but is equivalent to more than 4 m of global sea-level rise by the end of simulation period. By that time, surface conditions along the East Antarctic ice sheet margin take on characteristics of the present-day Greenland ice sheet. West Antarctic ice shelves have thinned considerably from subshelf melting and grounding lines have retreated over distances of several 100 km, especially for the Ross ice shelf. In the low concentration scenario, corresponding to a local warming of 3–4°C, polar ice-sheet melting proceeds at a much lower rate. For the first 1,200 years, the Antarctic ice sheet is even slightly larger than today on account of increased accumulation rates but contributes positively to sea-level rise after that. The Greenland ice sheet loses mass at a rate equivalent to 35 cm of global sea level rise during the first 1,000 years increasing to 150 cm during the last 1,000 years. For both scenarios, ice loss from the Antarctic ice sheet is still accelerating after 3,000 years despite a constant greenhouse gas forcing after the first 70–140 years of the simulation.