The mutation rate of a well adapted population is prone to reduction so as to have lower mutational load. The aim here is to understand the role of epistatic interactions in this process. Using a multitype branching process, the probability of fixation of a rare nonmutator in an asexual mutator population undergoing deleterious mutations at constant, but much higher rate than that of the nonmutator is analytically calculated here. We find that antagonistic epistasis lowers chances of mutation rate reduction, while synergistic epistasis enhances it. Below a critical value of epistasis, it can be seen that the fixation probability behaves nonmonotonically with variation in mutation rate of the background population for constant selection. Also, the variation of this critical value of epistasis parameter with the strength of the mutator is discussed. For synergistic epistasis, fixation probability shows a nonmonotonic trend with respect to selection when mutation rate is held constant.