In this paper, a rigid body controller is designed on the tangent bundle TSE(3) of the Lie group SE(3) using the backstepping technique. The controller is capable of treating the rotational and translational motions of the rigid body simultaneously. The system states considered in the control design are rotational and translational displacements and velocities of the body. As a result, the states of the system are composed of the 4×4 configuration tensor of the body and its six-dimensional augmented velocity vector. In addition, the use of geometric mechanics in the control design results in almost global asymptotic stability of the resulting motion which is proved via a Morse-Lyapunov-based approach.