The Most Reverend Justin Welby and the Pope met on Friday at the Vatican. The Archbishop of Canterbury was accompanied by his wife, Caroline, and the head of the Roman Catholic Church in England and Wales, Vincent Nichols.
In an address, Archbishop Welby said the Catholic Church and Anglican Communion were called "through fraternal love" to continue the dialogue of the last fifty years.
"I pray that the nearness of our two inaugurations may serve the reconciliation of the world and the Church," he said.
"As you have stressed, we must promote the fruits of our dialogue and, with our fellow bishops, we must give expression to our unity in faith through prayer and evangelisation.
"It is only as the world sees Christians growing visibly in unity that it will accept through us the divine message of peace and reconciliation."
The Archbishop admitted that the journey was "testing" and that the two Churches "cannot be unaware that differences exist about how we bring the Christian faith to bear on the challenges thrown up by modern society".
However, he said a firm foundation of friendship would enable them to be hopeful in speaking to each other about their differences and open to "sharing the discernment of a way forward that is faithful to the mind of Christ pressed upon us as disciples".
Archbishop Welby said the way forward should reflect the self-giving love of Christ, seen in hospitality and love for the poor, especially those affected by present crises around the world.
"Also, even as we speak, our brothers and sisters in Christ suffer terribly from violence, oppression and war, from bad government and unjust economic systems. If we are not their advocates in the name of Christ, who will be?" he said.
Pope Francis also spoke warmly of the opportunities for the two Churches to speak and work together to achieve greater social justice and a fairer economic system in the world.
"Among our tasks as witnesses to the love of Christ is that of giving a voice to the cry of the poor, so that they are not abandoned to the laws of an economy that seems at times to treat people as mere consumers," he said.
Other areas of cooperation suggested by the Pope included respect for the sacredness of life and marriage, and the promotion of Christian values "in a world that seems at times to call into question some of the foundations of society".
The Pope also acknowledged that the history of relations between the Church of England and the Catholic Church was "complex and not without pain".
"Recent decades, however, have been marked by a journey of rapprochement and fraternity, and for this we give heartfelt thanks to God," he continued. "These firm bonds of friendship have enabled us to remain on course even when difficulties have arisen in our theological dialogue that were greater than we could have foreseen at the start of our journey."
The Pope also said he was grateful for the "sincere efforts" of the Church of England to understand the reasons for the establishment of the ordinariate for former Anglicans.