Among the many ways that AI technologies are becoming embedded in our social worlds is the proliferation of Conversational User Interfaces, such as voice assistants (e.g. Apple Siri and Amazon Alexa), chatbots and voice-based conversational agents. Such conversational AI technologies are designed to draw upon the designers’ understanding of interactional practices employed in human–human conversation, and therefore have implications for intercultural communication (ICC). In this paper, we highlight some of the current shortcomings of conversational AI, and how these relate to ICC. We also draw on findings from Conversation Analysis to discuss how pragmatic norms vary across linguacultural groups (see Risager, Karen. 2019. Linguaculture. In Carol A. Chapelle (ed.). Encyclopedia of applied linguistics. Wiley-Blackwell for a discussion of the term ‘linguaculture’), noting that this poses further challenges for designers of conversational AI systems. We argue that the solution is to work towards what we call interculturally adaptive conversational AI. Finally, we propose a framework for how this can be conceptualised and researched, and argue that researchers with expertise in language and ICC are uniquely placed to contribute to this endeavour.