Conflict mediation requires reliably distinguishing the sources of disagreement as stemming from differences in beliefs about what is true (causality) vs. differences in what is valued (morality). The consequences of misdiagnosis -such as deadlock or escalation of conflict- can be significant, particularly in contexts related to sustainability and ethical management. Contributing to the rapidly developing literature on the use of Large Language Models (LLMs) to mediate contentious human discussions, we develop a conflict diagnosis competence test for LLMs to assess if they can differentiate disagreements rooted in causal and moral disagreements. We use a vignette study to apply the test to OpenAI’s GPT-3.5 and GPT-4. We find that both LLMs have similar semantic understandings of the distinction between causal and evaluative (moral) sources of disagreement as humans and can reliably distinguish between them, with GPT-4 performing better than GPT-3.5. However, compared to humans, both models exhibit a tendency to overestimate the extent of causal disagreement and underestimate the extent of moral disagreement in situations that feature moral misalignment. We conclude by discussing the implications for using LLMs to mediate conflict.