This article proposes a new method for the synthesis of autonomous underwater vehicles (AUVs) with a multilink manipulators control system, which provides for the automatic execution of contact manipulation operations by AUVs in stabilized hovering mode near or above target objects. To achieve the desired magnitude of the working tool’s force effect on the object surface, the force vector exerted by this tool is calculated. Next, control signals providing additional movements of the manipulator’s tool in the direction of the desired force vector are generated. Simultaneously, based on the calculated effects from the manipulator on the AUV, the thrusts of the latter’s thrusters create the necessary pull at the manipulator’s attachment point, which allows it to exert the desired force effects on the object surface. To compensate for the inevitable AUV stabilization system errors, leading to the tool’s deviations from the trajectory, the latter is automatically corrected, taking into account the actual AUV deviations. As a result, contact manipulation operations are performed while maintaining the continuous contact of the tool with the object, even with slight displacements of the AUV from the stabilization point. The operability and efficiency of the synthesized system are confirmed by the results of numerical modeling, with the use of basin experimental data and visualization.