This paper deals with the design of control schemes for a robot manipulator in contact with a compliant surface. A passivity-based approach is adopted in the task space, where the control law contains a nonlinear model-based term and a linear term obtained as the sum of a position action and a force action. The force control action dominates the position control action along the constrained task space direction so as to achieve force regulation at the expense of a steady-state position error. Motion control along the unconstrained task space directions is ensured. In the case of imperfect model compensation, the scheme is made adaptive with respect to a set of dynamic parameters. Numerical case studies are developed for an industrial robot manipulator.