We develop visual servo control to stabilize the image of moving soft tissue in B-mode ultrasound (US) imaging. We define the target region in a B-mode US image, and automatically control a robot to manipulate an US probe by minimizing the difference between the target and the most recently acquired US image. We exploit tissue speckle information to compute the relative pose between the probe and the target region. In-plane motion is handled by image region tracking and out-of-plane motion recovered by speckle tracking using speckle decorrelation. A visual servo control scheme is then applied to manipulate the US probe to stabilize the target region in the live US image. In a first experiment involving only translational motion, an US phantom was moved by one robot while stabilizing the target with a second robot holding the US probe. In a second experiment, large 6-DOF motions were manually applied to an US phantom while a 6-DOF medical robot was automatically controlled to compensate for the probe displacement. The obtained results support the hypothesis that automated motion stabilization shows promise for a variety of US-guided medical procedures such as prostate cancer brachytherapy.