This study investigates the physical processes and mechanisms driving the interannual variability of deep convective intensity in the Greenland Sea from 1993 to 2016. The intensity of deep convection is derived using the traditional Maximum Mixed Layer Depth, the total surface area with the monthly-mean mixed layer depth exceeding 800 m and various indices. All metrics show that the intensity of convection increased during the 2000s. The analysis demonstrates that observed increases of the deep convective intensity in the Greenland Sea is associated with an increase in the upper ocean salinity. The long-term interannual variability of deep convection is mainly linked to the variation of the water salinity during the preceding summer and the current winter. In turn, the variability of the upper-ocean salinity is primarily related to the variability in the advection of Atlantic water into the region with the re-circulating branches of the West Spitsbergen Current and to a lesser degree, to the local sea ice melt. For only two winters during the study period did the sea ice contribute significantly to a weakening of the intensity of deep convection by substantially reducing oceanic heat loss to the atmosphere. The variability in the advected heat is effectively abated by the concurrent variations of oceanic heat release to the atmosphere. The interplay between the interannual variability of the oceanic heat advection and the winter air-sea net heat flux leads to a noticeable reduction of the interannual variability of both fluxes over the convective regions. As a result, the direct effect of the varying air-sea heat exchange did not have a pronounced direct effect on the interannual variation in the intensity of deep convection in the Greenland Sea, at least during the study period.