Grid forming (GFM) inverter interfaced energy storage system can offer frequency support for islanded microgrids (IMGs), and the frequency response relies on the GFM inverter’s power output and power instruction interaction. However, droop control, a primary GFM method, faces challenges in reducing frequency deviations during significant disturbances due to the constant power instruction, potentially triggering the relay. To enhance the security of IMGs, this paper proposes a power instruction correction (PIC) based frequency response strategy for GFM inverter in IMGs. Firstly, the fundamental principle of the PIC strategy that originates the basic droop control is theoretically analyzed. When disturbances are insignificant, the PIC strategy maintains the basic droop control structure. In the event of a significant disturbance, the PIC strategy promptly corrects the active power instruction by estimating the disturbance approximately to reduce frequency deviations. Secondly, by analyzing specific operating modes and switching logic, the detailed implementation of the PIC strategy is presented. Finally, the superiority of the PIC strategy is verified through simulation and hardware-in-the-loop experiments.