With a numerical model we test the sensitivity of the Arctic Ocean circulation at mid-depth (212-1200 m) to the change in the sea ice rheology parameter P* that controls the sea ice compressive strength. We show that the reduction of the sea ice strength via P* within commonly used envelope reduces the sea ice extent and consequently enhances the ocean surface heat loss in the marginal ice zone. This leads to cooling of the Atlantic water inflow into the Arctic Ocean. As a result Eurasian Basin and Amerasian Basin temperatures are in average cooled by 0.1 °C and 0.05 °C, respectively. An increased sea ice drift speed in the central Arctic leads to an enhanced circulation of the anticyclonic Beaufort Gyre of the Amerasian Basin, which in turn weakens the cyclonic Atlantic water circulation below and enhances the recirculation of the Atlantic water in the Eurasian Basin. Consequently the balance of the volume fluxes through the Arctic gateways changes. Fram Strait net outflow increases by 0.46 Sv, Barents Sea Opening net inflow increases by 0.19 Sv and Davis Strait net outflow decreases by 0.28 Sv. This may spread the effects of the sea ice strength change beyond the limits of the Arctic Ocean and into the deep water convection zones in the North Atlantic. These substantial effects should be considered also in the model optimization efforts where P* is commonly used as one of the tuning parameters to achieve better sea ice simulations, whereas the effects on the ocean circulation are rarely taken into account.