Causal mediation analysis is used to decompose the total effect of an exposure on an outcome into an indirect effect, taking the path through an intermediate variable, and a direct effect. To estimate these effects, strong assumptions are made about unconfoundedness of the relationships between the exposure, mediator and outcome. These assumptions are difficult to verify in a given situation and therefore a mediation analysis should be complemented with a sensitivity analysis to assess the possible impact of violations. In this paper we present a method for sensitivity analysis to not only unobserved mediator-outcome confounding, which has largely been the focus of previous literature, but also unobserved confounding involving the exposure. The setting is estimation of natural direct and indirect effects based on parametric regression models. We present results for combinations of binary and continuous mediators and outcomes and extend the sensitivity analysis for mediator-outcome confounding to cases where the continuous outcome variable is censored or truncated. The proposed methods perform well also in the presence of interactions between the exposure, mediator and observed confounders, allowing for modeling flexibility as well as exploration of effect modification. The performance of the method is illustrated through simulations and an empirical example.