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Nonlinear model-predictive control has recently shown its practicability in robotics. However it remains limited in contact interaction tasks due to its inability to leverage sensed efforts. In this work, we propose a novel model-predictive control approach that incorporates direct feedback from force sensors while circumventing explicit modeling of the contact force evolution. Our approach is based on the online estimation of the discrepancy between the force predicted by the dynamics model and force measurements, combined with high-frequency nonlinear model-predictive control. We report an experimental validation on a torque-controlled manipulator in challenging tasks for which accurate force tracking is necessary. We show that a simple reformulation of the optimal control problem combined with standard estimation tools enables to achieve state-of-the-art performance in force control while preserving the benefits of model-predictive control, thereby outperforming traditional force control techniques. This work paves the way toward a more systematic integration of force sensors in model predictive control.