In this paper, we design a nonlinear controller for the kinematic model of an underactuated rigid spacecraft that ensures uniform, ultimately bounded (UUB) tracking provided the initial errors are selected sufficiently small. The result is achieved via a judicious formulation, of the spacecraft kinematics and the novel design of a Lyapunov-based controller. We also discuss how standard backstepping control techniques can be fused with the kinematic controller to solve the full-order regulation problem for an axisymmetric spacecraft.