Sea-level is expected to rise for a long time to come, even after stabilization of human-induced climatic warming. Here we use simulations with the Earth system model of intermediate complexity LOVECLIM to project sea-level changes over the third millennium forced with atmospheric greenhouse gas concentrations that stabilize by either 2000 or 2100 AD. The model includes 3D thermomechanical models of the Greenland and Antarctic ice sheets coupled to an atmosphere and an ocean model, a global glacier melt algorithm to account for the response of mountain glaciers and ice caps, and a procedure for assessing oceanic thermal expansion from oceanic heat uptake. Four climate change scenarios are considered to determine sea-level commitments. These assume a 21st century increase in greenhouse gases according to SRES scenarios B1, A1B and A2 with a stabilization of the atmospheric composition after the year 2100. One additional scenario assumes 1000 years of constant atmospheric composition from the year 2000 onwards. For our preferred model version, we find an already committed total sea-level rise of 1.1 m by 3000 AD. In experiments with greenhouse gas concentration stabilization at 2100 AD, the total sea-level rise ranges between 2.1 m (B1), 4.1 m (A1B) and 6.8 m (A2). In all scenarios, more than half of this amount arises from the Greenland ice sheet, thermal expansion is the second largest contributor, and the contribution of glaciers and ice caps is small as it is limited by the available ice volume of maximally 25 cm of sea-level equivalent. Additionally, we analysed the sensitivity of the sea-level contributions from an ensemble of nine different model versions that cover a large range of climate sensitivity realized by model parameter variations of the atmosphere–ocean model. Selected temperature indices are found to be good predictors for sea-level contributions from the different components of land ice and oceanic thermal expansion after 1000 years.