The robot manipulator is widely used in healthcare tasks owning to its advantages of the virus immunity, the intensive service capability, etc. For the safe and smooth robot-assisted healthcare task execution, real-time motion tracking controls and compliant physical human-robot interactions are concurrently important control objectives. In this work, the uncertainty and disturbance estimator (UDE)-based robust region tracking controller for a robot manipulator is developed. The regional feedback error is derived from the potential function to drive the robot manipulator end-effector converging into the target region, where the safe and compliant physical human-robot interaction can be achieved. Utilizing the back-stepping control approach, the regional feedback error is seamlessly integrated into the UDE-based control framework, where the UDE is employed to estimate and compensate unknown payloads, unmodeled dynamics and frictions. Due to the simple structure and strong robustness of the proposed method, only the minimum model information, i.e., a constant inertia matrix, is needed for implementation on multi-degrees of freedom robot manipulators without additional force/torque sensors. The Lyapunov method is used to analyze the stability of the closed-loop control system. With two 7 degrees of freedom(DoFs) redundant manipulators and one 6 DoFs nonredundant manipulator, experimental studies including 3D lemniscate trajectory tracking, human–robot interaction for bilateral rehabilitation and temperature measurement are carried out for controller effectiveness validation. Compared to benchmark adaptive region control method, the proposed approach achieves better robustness with 0.022 m less mean absolute errors and 0.022 m less root mean squared errors in the presence of model uncertainties. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.