In our previous research, we developed space robot teleoperation technology to achieve control from the ground of effective manual manipulations in orbit. To solve the communication time delay in the space robot teleoperation, we propose a mixed force and motion command-based space robot teleoperation system that is a model-based teleoperation. Moreover, we have also developed a compact 6-degree-of-freedom haptic interface as a master device. The important features of our teleoperation system are its robustness against modeling errors and its ability to realize the force exerted by the operator at the remote site. We introduce a new control method, which modified our model-based teleoperation system, to control the real robotic system Engineering Test Satellite VII manipulator. Surface-tracking and peg-in-hole tasks have been performed to confirm the effectiveness of our system. The experimental results obtained with our system including the haptic interface demonstrate its ability to perform these tasks in space without any major problems. We also evaluated different master device approaches for the model-based space teleoperation system. For this purpose, we used two methods, which are a master-slave (MS) approach and a force-joystick approach. Our results show that the MS approach is the best control method for contact tasks in which the directions of motion of the slave arm and of the operator's input force are different, as in the surface-tracking task.