Large language models (LLMs) have seen widespread adoption across various domains, yet their reliability is frequently undermined by hallucinations - responses that are plausible-sounding but factually incorrect. In high-stakes domains, these errors can reduce trust and introduce real-world risk. To address this challenge, we present a parameter-efficient approach that uses soft prompts to mitigate hallucinated content and promote responsible abstention in generative question-answering (QA) tasks. Our method, called Responsible Contrastive Soft Prompting (RCSP), uses a composite loss to train soft prompts that balance three goals: suppressing hallucinatory content, encouraging abstention under uncertainty, and preserving or improving factual recall. To achieve these goals, we incorporate contrastive loss, curriculum learning, and KL regularization into our training mechanism. We evaluate our approach on five diverse generative QA datasets using an LLM-as-a-Judge framework. Experimental results on the Gemma 3 (12B) and Llama 3.1 (8B) backbones demonstrate that RCSP effectively balances factual recall with hallucination suppression and abstention, yielding a generally superior F-score over standard reasoning and instruction-based prompting baselines. Notably, these improvements are achieved by training only a fraction of the parameters required by other tuning techniques. Our results demonstrate that soft prompts provide a modular and computationally efficient path toward improving LLM reliability.