Software aging often affects the performance of software systems and may eventually cause them to fail. A complementary approach to handle transient software failures due to the software aging is called software rejuvenation. It is a preventive and proactive solution that is particularly useful for counteracting the phenomenon of software aging. In this paper, we consider the optimal software rejuvenation policies maximizing the interval reliability using the Markov regenerative process formalism. We derive analytically the optimal software rejuvenation timing that maximizes the limiting interval reliability or the interval reliability with exponentially distributed operation time. Further, we examine numerically the transient behavior of the interval reliability at an arbitrary operation time. Our results under the interval reliability criteria are extensions of some earlier papers, since the interval reliability is a comprehensive measure that specializes to pointwise system availability and to system reliability.