This paper is devoted to the problem of global (local) stabilization of a prescribed subset of the state space for a passive affine nonlinear system. It is assumed that the desired attractive set can be described as an inverse image of zero value of some smooth nonnegative function, and that this function does not increase along the solutions of the unforced system. In terms of this function, a class of state feedback regulators and new sufficient conditions guaranteeing global (local) goal set stabilization are obtained.