“And I tell you, you are Peter, and on this rock I will build my church, and the powers of death shall not prevail against it. I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven.”
Short answer
Christ promises Peter the keys, prays for him by name so that he may strengthen the others, and charges him three times to feed the flock. In Acts Peter leads the choice of a new apostle, orders the baptism of the Gentiles in the house of Cornelius and speaks at the council in Jerusalem. Writers of the second and third centuries call him the rock on which the Church is built, and they list the bishops of Rome in succession from the apostles. In 431 the Roman legate told the Council of Ephesus that Peter lives and judges in his successors.
Built from the project document The Office of Peter as Vicar of Christ in the Catholic Church with His Successors. Every quotation was then checked against the linked source, and the wording and citations were changed to match that source where they differed. Four Scripture references are mislabeled in the project document and are shown here with the correct chapter and verse. The entries for the Council of Ephesus and the Catechism were added from primary sources.
Where this teaching appears on the Offshoots timelines: 15 June 1520, The Church's reply to Luther: propositions on the pope, the Church and purgatory.
16 quotations in date order
“Simon, Simon, behold, Satan demanded to have you, that he might sift you like wheat, but I have prayed for you that your faith may not fail; and when you have turned again, strengthen your brethren.”
“"Simon, son of John, do you love me more than these?" He said to him, "Yes, Lord; you know that I love you." He said to him, "Feed my lambs." … "Tend my sheep." … "Feed my sheep."”
“In those days Peter stood up among the brethren … "For it is written in the book of Psalms … 'His office let another take.'"”
“Then Peter declared, "Can any one forbid water for baptizing these people who have received the Holy Spirit just as we have?" And he commanded them to be baptized in the name of Jesus Christ.”
“And after there had been much debate, Peter rose and said to them, "Brethren, you know that in the early days God made choice among you, that by my mouth the Gentiles should hear the word of the gospel and believe."”
“Then after three years I went up to Jerusalem to visit Cephas, and remained with him fifteen days.”
“Let us set before our eyes the illustrious apostles. Peter, through unrighteous envy, endured not one or two, but numerous labours; and when he had at length suffered martyrdom, departed to the place of glory due to him.”
“The blessed apostles, then, having founded and built up the Church, committed into the hands of Linus the office of the episcopate. … To him succeeded Anacletus; and after him, in the third place from the apostles, Clement was allotted the bishopric. … In this order, and by this succession, the ecclesiastical tradition from the apostles, and the preaching of the truth, have come down to us.”
“And when I had come to Rome I remained there until Anicetus, whose deacon was Eleutherus. And Anicetus was succeeded by Soter, and he by Eleutherus. In every succession, and in every city that is held which is preached by the law and the prophets and the Lord.”
“…the blessed Peter, the chosen, the pre-eminent, the first of the disciples, for whom alone and Himself the Saviour paid tribute…”
“Was anything withheld from the knowledge of Peter, who is called the rock on which the church should be built, who also obtained the keys of the kingdom of heaven, with the power of loosing and binding in heaven and on earth?”
“And Peter, on whom the Church of Christ is built, against which the gates of hell shall not prevail … left only one epistle of acknowledged genuineness.”
“And although to all the apostles, after His resurrection, He gives an equal power … yet, that He might set forth unity, He arranged by His authority the origin of that unity, as beginning from one. Assuredly the rest of the apostles were also the same as was Peter, endowed with a like partnership both of honour and power; but the beginning proceeds from unity.”
“There is no doubt, and in fact it has been known in all ages, that the holy and most blessed Peter, prince (ἔξαρχος) and head of the Apostles, pillar of the faith, and foundation (θεμέλιος) of the Catholic Church, received the keys of the kingdom from our Lord Jesus Christ, the Saviour and Redeemer of the human race, and that to him was given the power of loosing and binding sins: who down even to today and forever both lives and judges in his successors. The holy and most blessed pope Cœlestine, according to due order, is his successor and holds his place”
“The Lord made Simon alone, whom he named Peter, the "rock" of his Church. He gave him the keys of his Church and instituted him shepherd of the whole flock. … This pastoral office of Peter and the other apostles belongs to the Church's very foundation and is continued by the bishops under the primacy of the Pope.”