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Temperature reconstructions from Greenland ice-sheet (GrIS) ice cores indicate the occurrence of more than 20 abrupt warmings during the last glacial period (LGP) known as Dansgaard-Oeschger (D-O) events. Although their ultimate cause is still debated, evidence from both proxy data and modelling studies robustly links these to reorganisations of the Atlantic Meridional Overturning Circulation (AMOC). During the LGP, the GrIS expanded as far as the continental shelf break and was thus more directly exposed to oceanic changes than in the present. Therefore oceanic temperature fluctuations on millennial timescales could have had a non-negligible impact on the GrIS. Here we assess the effect of millennial-scale oceanic variability on the GrIS evolution from the last interglacial to the present day. To do so, we use a three-dimensional hybrid ice-sheet-shelf model forced by subsurface oceanic temperature fluctuations, assumed to increase during D-O stadials and decrease during D-O interstadials. Since in our model the atmospheric forcing follows orbital variations only, the increase in total melting at millennial timescales is a direct result of an increase in basal melting. We show that the GrIS evolution during the LGP could have been strongly influenced by oceanic changes on millennial timescales, leading to oceanically induced ice-volume contributions above 1 m sea level equivalent (SLE). Also, our results suggest that the increased flux of GrIS icebergs as inferred from North Atlantic proxy records could have been triggered, or intensified, by peaks in melting at the base of the ice shelves resulting from increasing subsurface oceanic temperatures during D-O stadials. Several regions across the GrIS could thus have been responsible for ice mass discharge during D-O events, opening the possibility of a non-negligible role of the GrIS in oceanic reorganisations throughout the LGP.