Interactive feedback, where feedback flows in both directions between teacher and student, is more effective than traditional one-way feedback. However, it is often too time-consuming for widespread use in educational practice. While Large Language Models (LLMs) have potential for automating feedback, they struggle with reasoning and interaction in an interactive setting. This paper introduces CAELF, a Contestable AI Empowered LLM Framework for automating interactive feedback. CAELF allows students to query, challenge, and clarify their feedback by integrating a multi-agent system with computational argumentation. Essays are first assessed by multiple Teaching-Assistant Agents (TA Agents), and then a Teacher Agent aggregates the evaluations through formal reasoning to generate feedback and grades. Students can further engage with the feedback to refine their understanding. A case study on 500 critical thinking essays with user studies demonstrates that CAELF significantly improves interactive feedback, enhancing the reasoning and interaction capabilities of LLMs. This approach offers a promising solution to overcoming the time and resource barriers that have limited the adoption of interactive feedback in educational settings.