Among the different ethical and political approaches to handling cultural or ethnic conflicts within the state, especially regarding the rights of indigenous peoples, interculturality is the preferable alternative. Instead of reducing the idea of a conflict, ethnic conflict in this case, to a zero-sum struggle between universes of knowledge, each seeking to impose itself on the other from the very first interaction, an intercultural approach aims to facilitate the conditions that allow for the levelling of inherently unequal power relations, such as those between historically relegated subjects (indigenous peoples) and entrenched state institutions. These institutions are naturally reluctant to revisit, question, or transform their own paradigms, values, and understandings of fundamental rights. For this purpose, I first address certain problematic aspects regarding the operationalisation of interculturality in a real-life scenario, a scenario of normative pluralism and interlegality produced by cultural diversity. This scenario, in particular, is adverse to the ideal conditions of a horizontal and self-reflecting dialogue. Second, I discuss the distinctively intercultural function befitting an interculturally-minded Constitutional Court or any similar institution. In doing so, one should remain mindful of the fact that, as an adjudicative body acting as an impartial third in disputes, the terms of intercultural dialogue do not always square easily with the institutional functions and dynamics of a Court. Finally, I assess the case law and the practices of the Peruvian Constitutional Court in the light of interculturality, before proposing some conclusions on the dual potential of Constitutional Courts and their intercultural mission.