Final answer:
The medial rectus muscle adducts the eye and is innervated by the oculomotor nerve (CN III). This extraocular muscle is essential for the movement of the eyes towards the midline, which is an important aspect of gaze control.
Step-by-step explanation:
The muscle that adducts the eye and is innervated by CN III (oculomotor nerve) is the medial rectus muscle. This extraocular muscle is responsible for pulling the eye inward towards the nose. The oculomotor nerve controls not only the medial rectus but also other extraocular muscles excluding the lateral rectus, which is controlled by the abducens nerve, and the superior oblique, which is controlled by the trochlear nerve. Coordination of eye movements is essential for proper gaze control and involves a complex interplay between these cranial nerves and the brain stem.