In this paper we are concerned with the problem of rendering a nonlinear system passive and globally asymptotically stable via static state feedback when there is a direct input-output feedthrough. We extend the solution proposed in the literature if the output of the system is exclusively a function of the state, and show that, under standard regularity assumptions, the necessary and sufficient condition for a nonlinear system to be globally feedback equivalent to a passive one is that it is uniformly invertible with relative order 1 and weakly minimum phase.