Melchizedek was called a high priest as well as king of Salem.
Since the high priest was God's representative on Earth, it was inevitable that there was a correlation to Jesus Christ.
Genesis 14:17-20 established the tradition of the tithe:
17. After Abram returned from defeating Kedorlaomer and the kings allied with him, the king of Sodom came out to meet him in the Valley of Shaveh (that is, the King's Valley).
18. Then Melchizedek king of Salem brought out bread and wine. He was priest of God Most High,
19. and he blessed Abram, saying, "Blessed be Abram by God Most High, Creator of heaven and earth.
20. And blessed be God Most High, who delivered your enemies into your hand." Then Abram gave him a tenth of everything.
Verse 6 of Hebrews 5:5-10 quotes the last half of Psalm 110:4.
5. So Christ also did not take upon himself the glory of becoming a high priest. But God said to him, "You are my Son; today I have become your Father."
6. And he says in another place, "You are a priest forever, in the order of Melchizedek."
7. During the days of Jesus' life on earth, he offered up prayers and petitions with loud cries and tears to the one who could save him from death, and he was heard because of his reverent submission.
8. Although he was a son, he learned obedience from what he suffered
9. and, once made perfect, he became the source of eternal salvation for all who obey him
10. and was designated by God to be high priest in the order of Melchizedek.
Hebrews 6:19-20:
19. We have this hope as an anchor for the soul, firm and secure. It enters the inner sanctuary behind the curtain,
20. where Jesus, who went before us, has entered on our behalf. He has become a high priest forever, in the order of Melchizedek.
Hebrews 7:1-17:
1. This Melchizedek was king of Salem and priest of God Most High. He met Abraham returning from the defeat of the kings and blessed him,
2. and Abraham gave him a tenth of everything. First, his name means "king of righteousness"; then also, "king of Salem" means "king of peace."
3. Without father or mother, without genealogy, without beginning of days or end of life, like the Son of God he remains a priest forever.
4. Just think how great he was: Even the patriarch Abraham gave him a tenth of the plunder!
5. Now the law requires the descendants of Levi who become priests to collect a tenth from the people--that is, their brothers--even though their brothers are descended from Abraham.
6. This man, however, did not trace his descent from Levi, yet he collected a tenth from Abraham and blessed him who had the promises.
7. And without doubt the lesser person is blessed by the greater.
8. In the one case, the tenth is collected by men who die; but in the other case, by him who is declared to be living.
9. One might even say that Levi, who collects the tenth, paid the tenth through Abraham,
10. because when Melchizedek met Abraham, Levi was still in the body of his ancestor.
11. If perfection could have been attained through the Levitical priesthood (for on the basis of it the law was given to the people), why was there still need for another priest to come--one
in the order of Melchizedek, not in the order of Aaron?
12. For when there is a change of the priesthood, there must also be a change of the law.
13. He of whom these things are said belonged to a different tribe, and no one from that tribe has ever served at the altar.
14. For it is clear that our Lord descended from Judah, and in regard to that tribe Moses said nothing about priests.
15. And what we have said is even more clear if another priest like Melchizedek appears,
16. one who has become a priest not on the basis of a regulation as to his ancestry but on the basis of the power of an indestructible life.
17. For it is declared: "You are a priest forever, in the order of Melchizedek."