We introduce an interactive LLM-based framework designed to enhance the autonomy and robustness of domestic robots, targeting embodied intelligence. Our approach reduces reliance on large-scale data and incorporates a robot-agnostic pipeline that embodies an LLM. Our framework, InteLiPlan, ensures that the LLM's decision-making capabilities are effectively aligned with robotic functions, enhancing operational robustness and adaptability, while our human-in-the-loop mechanism allows for real-time human intervention when user instruction is required. We evaluate our method in both simulation and on the real robot platforms, including a Toyota Human Support Robot and an ANYmal D robot with a Unitree Z1 arm. Our method achieves a 95% success rate in the `fetch me' task completion with failure recovery, highlighting its capability in both failure reasoning and task planning. InteLiPlan achieves comparable performance to state-of-the-art LLM-based robotics planners, while using only real-time onboard computing. Project website: https://kimtienly.github.io/InteLiPlan.