With the rapid development of AI applications in the most important areas of economic, political and social life, the regime for the protection of fundamental rights has been significantly affected. This reality gives rise to initiatives for new legislation at international, supranational and national level. At the level of international law in particular, this legislation currently focuses on the formulation of general principles and guidelines. What is lacking is more specific regulation in situations where the introduction of AI causes uncertainty as to the protection of specific rights, particularly where conflicts arise between them. This article attempts to formulate proposals for such a more specific regulation, based on widely acknowledged principles of international law. Given that technological development and its impact on today’s societies know no national limitations, the adoption of this ‘next step’ in international law may well determine the smooth adaptation of AI to the values of democratic societies.