4 This is a specific duty of the Bishop of Rome as the Successor of the Apostle Peter. I carry out this duty with the profound conviction that I am obeying the Lord, and with a clear sense of my own human frailty. Indeed, if Christ himself gave Peter this special mission in the Church and exhorted him to strengthen his brethren, he also made clear to him his human weakness and his special need of conversion: "And when you have turned again, strengthen your brethren" ( Lk 22:32). It is precisely in Peter's human weakness that it becomes fully clear that the Pope, in order to carry out this special ministry in the Church, depends totally on the Lord's grace and prayer: "I have prayed for you that your faith may not fail" ( Lk 22:32). The conversion of Peter and that of his Successors is upheld by the very prayer of the Redeemer, and the Church constantly makes this petition her own. In our ecumenical age, marked by the Second Vatican Council, the mission of the Bishop of Rome is particularly directed to recalling the need for full communion among Christ's disciples. The Bishop of Rome himself must fervently make his own Christ's prayer for that conversion which is indispensable for "Peter" to be able to serve his brethren. I earnestly invite the faithful of the Catholic Church and all Christians to share in this prayer. May all join me in praying for this conversion! We know that during her earthly pilgrimage the Church has suffered and will continue to suffer opposition and persecution. But the hope which sustains her is unshakable, just as the joy which flows from this hope is indestructible. In effect, the firm and enduring rock upon which she is founded is Jesus Christ, her Lord.
Source: Ut Unum Sint (Vatican.va)