Rare disease (RD) registries aim to promote data collection and sharing, and facilitate multidisciplinary collaboration with the overall aim of improving patient care. Recommendations relating to the minimum standards necessary to develop and maintain high quality registries are essential to ensure high quality data and sustainability of registries. The aim of this international study was to survey RD registry leaders to ascertain the level of consensus amongst the RD community regarding the quality criteria that should be considered essential features of a disease registry. Of 35 respondents representing 40 RD registries, over 95% indicated that essential quality criteria should include establishment of a good governance system (ethics approval, registry management team, standard operating protocol and long-term sustainability plan), data quality (personnel responsible for data entry and procedures for checking data quality) and construction of an IT infrastructure complying with Findable, Accessible, Interoperable and Reusable (FAIR) principles to maintain registries of high quality, with procedures for authorized user access, erasing personal data, data breach procedures and a web interface. Of the 22 registries that performed a self-assessment, over 80% stated that their registry had a leader, project management group, steering committee, active funding stream, website, and user access policies. This survey has acceptability amongst the RD community for the self-quality evaluation of RD registries with high levels of consensus for the proposed quality criteria.