In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only H(r) (K) boolean AND (H) over tilde (-1/2) (div, K)-regularity (r > 0) on the reference element (either triangle or square) K. We show that this operator is stable with respect to polynomial degrees and satisfies the commuting diagram property. We also establish an estimate for the interpolation error in the norm of the space (H) over tilde (-1/2) (div, K), which is closely related to the energy spaces for boundary integral formulations of time-harmonic problems of electromagnetics in three dimensions.