In recent years, embedded real-time systems have grown in complexity and are required to be able to handle both periodic and aperiodic tasks. When an external interrupt occurs via an I/O peripheral, the program counter jumps to the corresponding exception vector. This results in large overhead due to context switching. However, embedded real-time systems are required to execute tasks in real-time with high precision. The Responsive Multithreaded Processor (RMTP), a prioritized SMT CPU, consists of eight hardware contexts treated as eight logical processing cores and has various hardware mechanisms for fine-grained real-time processing on the order of 10 μs. One hardware mechanism implemented in RMTP is an interrupt wake-up mechanism that enables interrupt-triggered thread wake ups. When a thread is designated to be an interrupt handling thread, it starts execution one clock cycle after an interrupt occurs. In this paper, we design and implement a software mechanism which reduces the interrupt response time by using this mechanism and demonstrate the effectiveness of our proposed method by RTL simulations. Evaluation results show that our proposed method achieves high real-time performance by reducing the interrupt response time by up to 82% compared to the baseline.