Background: Autonomous grasping of soft tissues can facilitate the robotic surgery procedures. The previous attempts for implementing auto-grasping have been based on a simplistic representation of the actual surgery maneuvers. Method: A generalized three-zone grasp model was introduced to consider the effect of the pull force angulation on the grasp mode, that is, damage, slip, or safe grasp. Also, an extended auto-grasping algorithm was proposed in which the trigger force is automatically controlled against the pull force magnitude and direction, to achieve a safe and secure grasp. Results: The autonomous grasping experiments against a varying pull force in a phantom study indicated a good agreement between the desired and actual pinch and trigger forces (root mean square errors lower than 0.168 N and 0.280 N, respectively) and no sign of tissue tear or slippage. Conclusions: The proposed auto-grasping algorithm can help manipulating the soft tissues safely and effectively during robotic surgery procedures.