Yes, both Christian scripture and Islamic theology completely agree that Jesus was explicitly sent by God as a divinely appointed guide, teacher, and messenger to humanity.
In the New Testament gospels, his mission is framed as bringing spiritual salvation, healing the sick, and declaring the immediate arrival of the Kingdom of God. Similarly, the Quran defines his core task as delivering the Gospel (Injeel) and serving as a miraculous sign to guide the Children of Israel back to pure monotheistic worship.