With generative AI advancing, empathy in human-AI interaction is essential. While prior work focuses on emotional reflection, emotional exploration, key to deeper engagement, remains overlooked. Existing LLMs rely on text which captures limited emotion nuances. To address this, we propose RE-LLM, a speech-LLM integrating dimensional emotion embeddings and auxiliary learning. Experiments show statistically significant gains in empathy metrics across three datasets. RE-LLM relatively improves the Emotional Reaction score by 14.79% and 6.76% compared to text-only and speech-LLM baselines on ESD. Notably, it raises the Exploration score by 35.42% and 3.91% on IEMOCAP, 139.28% and 9.83% on ESD, and 60.95% and 22.64% on MSP-PODCAST. It also boosts unweighted accuracy by 5.4% on IEMOCAP, 2.3% on ESD, and 6.9% on MSP-PODCAST in speech emotion recognition. These results highlight the enriched emotional understanding and improved empathetic response generation of RE-LLM.