To foster research integrity (RI), it is necessary to address the institutional and system-of-science factors that influence researchers' behavior. Consequently, research performing and research funding organizations (RPOs and RFOs) could develop comprehensive RI policies outlining the concrete steps they will take to foster RI. So far, there is no consensus on which topics are important to address in RI policies. Therefore, we conducted a three round Delphi survey study to explore which RI topics to address in institutional RI policies by seeking consensus from research policy experts and institutional leaders. A total of 68 RPO and 52 RFO experts, representing different disciplines, countries and genders, completed one, two or all rounds of the study. There was consensus among the experts on the importance of 12 RI topics for RPOs and 11 for RFOs. The topics that ranked highest for RPOs concerned education and training, supervision and mentoring, dealing with RI breaches, and supporting a responsible research process (e.g. through quality assurance). The highest ranked RFO topics concerned dealing with breaches of RI, conflicts of interest, and setting expectations on RPOs (e.g. about educating researchers about RI). Together with the research policy experts and institutional leaders, we developed a comprehensive overview of topics important for inclusion in the RI policies of RPOs and RFOs. The topics reflect preference for a preventative approach to RI, coupled with procedures for dealing with RI breaches. RPOs and RFOs should address each of these topics in order to support researchers in conducting responsible research.