A Muslim Must Spread Islam

"O Messenger! Make known (balagh) all that has been sent down to thee by thy Lord and Sustainer." (5:67)

"Invite to the way of your Lord with wisdom and good instruction, and argue with them in a way that is best." (Quran 16:125)

"He it is who has sent to the unlettered people a Messenger from among themselves to convey unto them His messages, and to lead them to purity and spiritual growth (tazkiyah) and to teach them the Book and the Wisdom (ta'lim)..." (62:2)

Balagh, da'wah and ta'lim are also mentioned in the Qur'an and Hadith as duties of Muslims generally:

"Convey from me (balagh) even if it be only a single ayah (that you know)." (Bukhari)

"Let there among you be a group that invites to all that is good (da'wah)." (3:104)

"Say! This is my way. I call to God (da'wah) — on the basis of sure knowledge — I and those who (truly) follow me. Glory to God and I am not among those who commit shirk." (12:108)

"Acquire knowledge and teach it to mankind (ta'lim), learn your religious duties and teach them to mankind, learn the Qur'an and teach it to mankind, for I am a man who will be taken away..." (Darimi)

An Islamic source: The Work of Propagation of Islam.