The ability to actively apply contractile forces to their environment and to sense its mechanical properties are fundamental features of cells. The widespread view is that contractile forces are mechanosensitive, i.e. that cells regulate these forces through sensing the rigidity of the environment. Here we use theory and extensive experiments to study the time evolution of cellular contractile forces. We show that they are generated by an intrinsic, time-dependent contractile displacement that is independent of the environment’s rigidity. Consequently, whereas contractile forces indeed depend on the environment’s rigidity and in fact linearly scale with it, they do so through a purely mechanistic linear force-rigidity relation, i.e. in a non-mechanosensitive manner. Furthermore, we show that the force-generating contractile displacement is directly related to the evolution of the actomyosin network, most notably to the time-dependent concentration of F-actin. The emerging picture of force generation and mechanosensitivity unifies various existing observations on cellular contractility.