So far most of the research on the control task of free-floating space manipulators (FFSMs) has focused on the end-effector trajectory tracking, yet, has not considered the spacecraft attitude which acts as the base of the system. Nevertheless, it is of importance to keep the spacecraft attitude unchanged when the space manipulator is executing on-orbit servicing. Thus, a passivity based adaptive extended Jacobian controller for FFSMs with dynamic and kinematic uncertainties is proposed in this work. In order to fulfill the spacecraft attitude regulating and the manipulator trajectory tracking, a new Jacobian matrix is defined, which is called extended Jacobian matrix. Then a coordinated controller is proposed, in which a feedback term involved transposed Jacobian and a compensation term involved dynamics are involved. In virtue of Lyapunov-like analysis, the parameter updating laws and the stability of the controller are derived. Simulation are provided to illustrate the validity of the controller investigated in this work.