Existing target pursuit systems are able to coordinate a team of mobile agents to capture or intercept unauthorized targets. Multi-agent reinforcement learning (MARL) further empowers pursuit strategies with the potential to emerge complex behaviors. However, existing solutions lack the ability to handle the perception uncertainty caused by relative position measurement noises, which blurs the understanding of the target's state and complicates the pursuit strategy learning process. This study proposes PUARL, which enhances the learning under the perception uncertainty process by guiding exploration with probabilistic estimation and adapting the policy based on awareness of perception uncertainty. We validate its performance in terms of both accuracy and efficiency. PUARL achieves a success rate increase of 12.3%+ and a reduction in total steps by 58.3%+, outperforming both state-of-the-art heuristic and learning-based solutions.