This paper proposes an accuracy enhancement to the Model Reference Adaptive System-Current-Current (MRAS-CC) method for speed-sensorless control in the induction motor drive. The fundamental principle of the MRAS-CC method involves adjusting the difference between the virtual current and the measured current to determine the motor speed. However, the estimation model of the virtual current depends on the accuracy of the machine parameters, particularly changes in stator and rotor resistance due to heating during operation. This research proposes integrating simultaneous estimation of stator and rotor resistances into the speed estimation process of the typical MRAS-CC technique. This integration enhances the accuracy of the virtual current component in the MRAS-CC method, thereby improving motor performance. Three methods, including MRAS-CC, MRAS-CC with integrated stator resistance, and the proposed MRAS-CC, are implemented in MATLAB/Simulink. The proposed method reduces the ITAE speed from 25.43 (typical MRAS-CC) and 1.052 (MRAS-CC with R_s estimation) to 0.09969, while decreasing the speed overshoot to 0.03425%. Simulation results are used to verify and demonstrate the performance of the proposed MRAS-CC method in motor speed sensorless control.