This paper discusses the design of a teleoperated system for robotic-assisted surgery with haptic feedback. The operational space controller has a position-position teleoperation architecture with the phantom in the loop, enabling telepresence in free-space and contact. The performance of the robotic-assisted surgery with haptic feedback system is improved thanks to the stability and telepresence analysis. In free space, the surgeon feels the motion of the robot. When contact with tissues occurs, an on-line environment stiffness estimation is performed using an Extended Kalman Filter with robot modeling error compensation and without considering the contact position. Based on stability and transparency's frequency analysis, the estimated parameter is used to tune the teleoperation scheme in order to improve telepresence. The quality of telepresence allows the surgeon to perform and better characterize contact with different properties tissues. The null space control guarantees that surgical kinematic constraints are fulfilled. Both task and posture control run active observers (AOBs) in Cartesian domain, taking into account force, velocity and position signals. Experiments with our D2M2 (direct drive medical manipulator) robot are presented. To assess the proposed teleoperation scheme, ex-vivo tissues are exhibited