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The last glacial period (LGP; ca. 110-10 kyr BP) was marked by the existence of two types of abrupt climatic changes, Dansgaard-Oeschger (DO) and Heinrich (H) events. Although the mechanisms behind these are not fully understood, it is generally accepted that the presence of ice sheets played an important role in their occurrence. While an important effort has been made to investigate the dynamics and evolution of the Laurentide ice sheet (LIS) during this period, the Eurasian ice sheet (EIS) has not received much attention, in particular from a modeling perspective. However, meltwater discharge from this and other ice sheets surrounding the Nordic seas is often implied as a potential cause of ocean instabilities that lead to glacial abrupt climate changes. Thus, a better comprehension of the evolution of the EIS during the LGP is important to understand its role in glacial abrupt climate changes. Here we investigate the response of the EIS to millennial-scale climate variability during the LGP. We use a hybrid, three-dimensional, thermo-mechanical ice-sheet model that includes ice shelves and ice streams. The model is forced off-line via a novel perturbative approach that, as opposed to conventional methods, clearly differentiates between the spatial patterns of millennial-scale and orbital-scale climate variability. Thus, it provides a more realistic treatment of the forcing at millennial timescales. The effect of both atmospheric and oceanic variations are included. Our results show that the EIS responds with enhanced ice discharge in phase with interstadial warming in the North Atlantic when forced with surface ocean temperatures. Conversely, when subsurface ocean temperatures are used, enhanced ice discharge occurs both during stadials and at the beginning of the interstadials. Separating the atmospheric and oceanic effects demonstrates the major role of the ocean in controlling the dynamics of the EIS on millennial timescales. While the atmospheric forcing alone is only able to produce modest iceberg discharges, warming of the ocean leads to higher rates of iceberg discharges as a result of relatively strong basal melting at the margins of the ice sheet. Our results clearly show the capability of the EIS to react to glacial abrupt climate changes, and highlight the need for stronger constraints on the ice sheet's glacial dynamics and climate-ocean interactions.