Advances in omics and specifically genomic technologies are increasingly transforming rare disease diagnosis. However, the benefits of these advances are disproportionately experienced within and between populations, with Indigenous populations frequently experiencing diagnostic and therapeutic inequities. The International Rare Disease Research Consortium (IRDiRC) multi-stakeholder partnership has been advancing toward the vision of all people living with a rare disease receiving an accurate diagnosis, care, and available therapy within 1 year of coming to medical attention. In order to further progress toward this vision, IRDiRC has created a taskforce to explore the access barriers to diagnosis of rare genetic diseases faced by Indigenous peoples, with a view of developing recommendations to overcome them. Herein, we provide an overview of the state of play of current barriers and considerations identified by the taskforce, to further stimulate awareness of these issues and the passage toward solutions. We focus on analyzing barriers to accessing genetic services, participating in genomic research, and other aspects such as concerns about data sharing, the handling of biospecimens, and the importance of capacity building.