As climate change and other global challenges increase the likelihood of unforeseen emergencies, the limitations of human-driven strategies in critical situations become more pronounced. Inadequate pre-established emergency plans can lead operators to become overwhelmed during complex systems malfunctions. This study addresses the urgent need for agile decision-making in response to various unforeseen incidents through a novel approach, EvoTaskTree (a task-driven method with evolvable interactive agents using event trees for emergency decision support). This advanced approach integrates two types of agents powered by large language models (LLMs): task executors, responsible for executing critical procedures, and task validators, ensuring the efficacy of those actions. By leveraging insights from event tree analysis, our framework encompasses three crucial tasks: initiating event subevent analysis, event tree header event analysis, and decision recommendations. The agents learn from both successful and unsuccessful responses from these tasks. Finally, we use nuclear power plants as a demonstration of a safety-critical system. Our findings indicate that the designed agents are not only effective but also outperform existing approaches, achieving an impressive accuracy rate of up to 100 % in processing previously unencoun32 tered incident scenarios. This paper demonstrates that EvoTaskTree significantly enhances the rapid formulation of emergency decision-making.