In this article, a robust adaptive impedance control based on the modified function approximation technique, and augmented with a novel integral nonsingular terminal sliding mode control, is proposed for a surgical haptic system. The haptic device is maneuvered by surgeons, whereby the mode of action, motion path, and haptic dynamics are rendered as unknowns. The inclusion of integral nonsingular terminal sliding mode control leverages the capability of ensuring consistent tracking of system’s trajectories performance, fast transient response, finite-time convergence, improved robustness, and reduced chattering. However, the modified function approximation technique strategy allows to estimate model’s dynamics regardless of the availability of dynamic uncertainties’ lower and upper bounds. In addition, an estimate of the intended motion mode and path is integrated in the evolved adaptive impedance control, via radial basis function neural network, permitting the haptic arm to track the target impedance model. Finally, using the haptic arm, controlled experimental cases and comparative study were done, after which the proposed surgical simulator adopted the results for real-time validation.