Robots capable of assisting elderly people in their homes will become indispensable, since the world population is aging at an alarming rate. A crucial requirement for these robotic caregivers will be the ability to safely interact with humans, such as firmly grasping a human arm without applying excessive force. Minding this concern, we developed a reactive grasp that, using tactile sensors, monitors the pressure it exerts during manipulation. Our approach, inspired by human manipulation, employs an architecture based on different grasping phases that represent particular stages in a manipulation task. Within these phases, we implemented and composed simple components to interpret and react to the information obtained by the tactile sensors. Empirical results, using a Care-O-bot 3 R with a Schunk Dexterous Hand (SDH-2), show that considering tactile information can reduce the force exerted on the objects significantly.