In applications where robot manipulators are in contact with the environment, better known as constrained-motion applications, it is necessary to have a control algorithm that guarantees a suitable interaction between the robot and its environment. The main interaction control schemes in task-space require accurate knowledge of the dynamics of the system to be controlled; then, if the parameters of the environment and the robotic system are unknown, it is essential to use adaptive control schemes. This paper presents an adaptive stiffness control scheme for robot manipulators, that allows to solve the problem of interaction control in the face of parametric uncertainty about the stiffness of the environment and the gravitational forces acting on the robot. The control structure is based on a regressor to estimate the unknown parameters and it is supported by a stability analysis, in the Lyapunov sense, to demonstrate the asymptotic stability of the equilibrium point of the closed-loop system. Finally, some results obtained in simulation are presented in order to verify the correct performance of the proposed control structure.