This paper presents a novel slip-suppression controller for a two-fingered robotic manipulator, where the goal is to minimize the slip distance without using excessive force. To do this, we consider monotonic PI (MPI) control, which is a nonlinear extension of linear proportional-integral (PI) control. The advantage of MPI control is the fact that the normal force of the gripper is prohibited from decreasing during the transition from predominantly proportional control to predominantly integral control as occurs in the case of linear PI control. The performance of the MPI control is compared to linear PI control for a range of controller parameters, and the tradeoff between the maximum normal force and the total slip distance is efficiently captured by Pareto-front analysis. The robustness of MPI is assessed by considering uncertainty in the body mass and friction parameters, as well as the effect of measurement noise and actuator dynamics.