Malachi gives a prophecy that Elijah the prophet would come before the Messiah arrived:

Look, I will send you Elijah the prophet before the great and terrible day of the LORD arrives.Malachi 4:5

Jesus identified John the Baptist as the fulfillment of the prophecy of Elijah:

13 For all the prophets and the law prophesied until John appeared. 14 And if you are willing to accept it, he is Elijah, who is to come.Matthew 11:13-14, cf. Matthew 17:12-13, Mark 9:13

Yet John denied being Elijah:

So they asked him, "Then who are you? Are you Elijah?" He said, "I am not!" "Are you the Prophet?" He answered, "No!"Malachi 4:5

There is no contradiction here. John the Baptist was not Elijah reincarnated or resurrected. John the Baptist was Elijah in that he was a great prophet speaking to Israel:

"And he will go as forerunner before the Lord in the spirit and power of Elijah, to turn the hearts of the fathers back to their children and the disobedient to the wisdom of the just, to make ready for the Lord a people prepared for him."Luke 1:17, emphasis mine

There is no contradiction. John the Baptist was not Elijah himself, but came "in the spirt and power of Elijah".