PurposeRisk management (RM) functions are expected to become more involved in environmental and sustainability activities, yet a serious lack of quantitative evidence exists on these links. This study aims to explore the direct link between RM functions as one aspect of internal audit functions and green process innovation (GP), sustainability performance (SP) and the indirect link between RM functions of internal audits and SP through the mediation of GP. The study also explores whether the impact of RM functions of internal audits on GP strengthens with the emergence of green transformational leadership (GT) and green knowledge sharing (GK).Design/methodology/approachPrimary data were collected through a survey of the opinions of 197 internal audit managers in Vietnamese manufacturing firms and analyzed by partial least squares structural equation modeling.FindingsThe results revealed interesting findings. First, RM functions of internal audits are a driving force for the Vietnamese manufacturing sector to strengthen GP and SP. Second, the relationship between RM functions of internal audits and GP is strengthened when manufacturing firms own GT as well as promote GK. Third, GP is like a bridge to transform the value of RM functions of internal audits toward SP. This result is an important basis for manufacturing firms to promote internal audits as well as promote the role of RM functions in identifying environmental risks, thereby enhancing green manufacturing toward sustainable development. The results also encourage GT and GK to exert positive effects as catalysts to improve the influence of RM functions of internal audits on GP.Originality/valueThis study contributes significantly to the existing literature by identifying the relationship between RM functions of internal audits, GP and SP, as well as the moderating roles of GT and GK in this relationship. Furthermore, this is one of the few studies that has successfully investigated the mediating function of GP in the indirect effect of RM functions of internal audits on SP.