The etch rate of silicon nitride (Si3N4) in the afterglow of fluorine-containing plasmas is strongly enhanced when both nitrogen and oxygen are added to the remote discharge. This effect is attributed to the formation of nitric oxide (NO), which we identify as a highly reactive precursor for the etching of Si3N4. The Si3N4 etch rate, surface oxidation, and the depletion of the surface of N atoms show a linear dependence on the NO density. In order to determine the products of the NO reaction at the Si3N4 surface, mass spectrometry was performed in immediate proximity to the surface with a specially designed movable sampling orifice. Both SiF4 and N-2 are identified as primary etch products, but a smaller amount of N2O was also detected. Based on our results, we suggest that NO enhances the removal of N from the Si3N4 surface by the formation of gaseous N-2, and leaving behind an O atom, while the overall surface oxidation remains very low, and the reactive layers are very thin. This modified surface reacts more readily with F atoms than the Si3N4 surface.