A high-precision manipulation task, such as needle threading, is challenging. Physiological studies have proposed connecting low-resolution peripheral vision and fast movement to transport the hand into the vicinity of an object, and using high-resolution foveated vision to achieve the accurate homing of the hand to the object. The results of this study demonstrate that a deep imitation learning based method, inspired by the gaze-based dual resolution visuomotor control system in humans, can solve the needle threading task. First, we recorded the gaze movements of a human operator who was teleoperating a robot. Then, we used only a high-resolution image around the gaze to precisely control the thread position when it was close to the target. We used a low-resolution peripheral image to reach the vicinity of the target. The experimental results obtained in this study demonstrate that the proposed method enables precise manipulation tasks using a general-purpose robot manipulator and improves computational efficiency.