The viscoelastic response of living cells to small external forces and deformations is characterized by a weak power law in time. The elastic modulus of cells and the power law exponent with which the elastic stresses decay depend on the active contractile prestress in the cytoskeleton. It is unknown whether this also holds in the physiologically relevant regime of large external forces and deformations. We used magnetic tweezers to apply stepwise increasing forces to magnetic beads bound to the cytoskeleton of different cell lines, and recorded the resulting cell deformation (creep response). The creep response followed a weak power law at all force levels. Stiffness and power law exponent increased with force in all cells, indicating simultaneous stress stiffening and fluidization of the cytoskeleton. The amount of stress stiffening and fluidization differed greatly between cell types but scaled with the contractile prestress as the only free parameter. Our results demonstrate that by modulating the internal mechanical tension, cells can actively control their mechanical properties over an exceedingly large range. This behavior is of fundamental importance for protection against damage caused by large external forces, and allows the cells to adapt to the highly variable and nonlinear mechanical properties of the extracellular matrix.