John 1:21

They asked him, “Then who are you? Are you Elijah?” He said, “I am not.” “Are you the Prophet?” He answered, “No.”

Since he claimed to not be the Christ, the delegation had a few more questions to ask him:

They asked him if he was Elijah because prophecy had it that Elijah would return to precede the coming of the Messiah. (Mal 4:5) Jesus later stated that this was John (Matt 11:14), and yet John denied it. There are at least 2 explanations for his response to this question:

Malachi 4:5  “See, I will send you the prophet Elijah before that great and dreadful day of the LORD comes.

Matthew 11:14  And if you are willing to accept it, he is the Elijah who was to come.

  1. He answered what they asked.  The Jews remembered that Elijah had left the earth in a chariot of fire without experiencing death, and they expected him to return in fulfillment of the prophecy, but John was not Elijah, he was John.  The person of Elijah did not return. John was Elijah, but not in the sense of being identical to the person of Elijah; he was a prophet in the spirit of Elijah, which was what the prophecy was predicting.
  2. John didn’t know who he was.  Just because Jesus knew who John was does not mean that John knew.  This can have relevance for us, too.  As Morris points out, “No man is what he himself thinks he is.  He is only what Jesus knows him to be.” (NICNT 135-6)

They also asked him if he was the Prophet.  Prophecy had ceased for many years, and the Jews expected the coming of the Messiah to be preceded by the advent of many prophets, but most especially the prophet foretold in (Deut 18:15-18) whom they thought to be distinct from the Christ, but in hindsight we know that prophet is Jesus. Acts 3:19-23

Deuteronomy 18:15-18  The LORD your God will raise up for you a prophet like me from among your own brothers. You must listen to him. For this is what you asked of the LORD your God at Horeb on the day of the assembly when you said, “Let us not hear the voice of the LORD our God nor see this great fire anymore, or we will die.” The LORD said to me: “What they say is good. I will raise up for them a prophet like you from among their brothers; I will put my words in his mouth, and he will tell them everything I command him.

Acts 3:19-23  Repent, then, and turn to God, so that your sins may be wiped out, that times of refreshing may come from the Lord, and that he may send the Christ, who has been appointed for you—even Jesus. He must remain in heaven until the time comes for God to restore everything, as he promised long ago through his holy prophets.  For Moses said, ‘The Lord your God will raise up for you a prophet like me from among your own people; you must listen to everything he tells you.  Anyone who does not listen to him will be completely cut off from among his people.’

Note the increasing curtness of John’s replies.  He had come to bear witness to another, not to answer questions about himself.