Large language models (LLMs) show promise in offering emotional support and generating empathetic responses for individuals in distress, but their ability to deliver culturally sensitive support remains underexplored due to a lack of resources. In this work, we introduce , the first dataset designed for this task, spanning four cultures and including 1,729 distress messages, 1,523 cultural signals, and 1,041 support strategies with fine-grained emotional and cultural annotations. Leveraging , we (i) develop and test four adaptation strategies for guiding three state-of-the-art LLMs toward culturally sensitive responses; (ii) conduct comprehensive evaluations using LLM-as-a-Judge, in-culture human annotators, and clinical psychologists; (iii) show that adapted LLMs outperform anonymous online peer responses, and that simple cultural role-play is insufficient for cultural sensitivity; and (iv) explore the application of LLMs in clinical training, where experts highlight their potential in fostering cultural competence in novice therapists.