Violent intergroup conflicts continue to be one of the most pressing issues of our time. One key factor that instigates and perpetuates conflict is people’s support for violence against the outgroup. Thus, understanding the psychology behind such support is essential for developing strategies to reduce conflict. In this Review, we offer a new umbrella term, the conflict-supporting mindset (CSM), to tie together findings across the extensive literature on the psychology of conflict. A CSM captures a set of interrelated negative attitudes, feelings and beliefs regarding the outgroup, which devalues and demonizes its members. As such, a CSM is pivotal in making violence seem permissible and even necessary. We consider the sources of a CSM: basic cognitive and motivational roots, personal inclinations, group-level influences, situational influences and post-hoc justifications of violence. We then discuss conflict reduction interventions that draw on the psychology underlying a CSM. Finally, we reflect on the limitations of efforts towards conflict reduction, both from a practical and an ethical perspective, and suggest directions for future research.