Large Language Models (LLMs) have demonstrated remarkable performance across various information-seeking and reasoning tasks. These computational systems drive state-of-the-art dialogue systems, such as ChatGPT and Bard. They also carry substantial promise in meeting the growing demands of mental health care, albeit relatively unexplored. As such, this study sought to examine LLMs' capability to generate empathetic responses in conversations that emulate those in a mental health counselling setting. We selected five LLMs: version 3.5 and version 4 of the Generative Pre-training (GPT), Vicuna FastChat-T5, Pathways Language Model (PaLM) version 2, and Falcon-7B-Instruct. Based on a simple instructional prompt, these models responded to utterances derived from the EmpatheticDialogues (ED) dataset. Using three empathy-related metrics, we compared their responses to those from traditional response generation dialogue systems, which were fine-tuned on the ED dataset, along with human-generated responses. Notably, we discovered that responses from the LLMs were remarkably more empathetic in most scenarios. We position our findings in light of catapulting advancements in creating empathetic conversational systems.