Francis urged Welby to continue proclaiming "the importance of the institution of the family built on marriage, a value that you yourself have had occasion to recall recently."
Former oil executive Welby, who was enthroned as Archbishop of Canterbury in March just weeks after Francis was elected pope, earlier this month tore into the British government's gay marriage bill.
Accompanied by his wife Caroline, Welby prayed with the pope and around one hundred representatives of the two Churches, including disaffected Anglicans who have joined the Catholic Church's ranks.
Welby said he "felt at home" at the Vatican, and hoped that "the closeness of the two inaugurations may serve the reconciliation of the world and the Church" -- an apparent reference to the leaders' common desire to tackle secularism by going out into the streets and meeting the people.
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Both Welby and Francis spoke of the importance of reaching out to the world's disadvantaged.
The Argentine pope called on Welby to help give "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."
The spiritual head of the world's 80 million Anglicans is known for taking the bus and has reportedly turned up to media interviews in clothes from charity shop Oxfam and shoes with holes in them.
The 57-year-old said "we must love above all those tossed aside, even whole nations, by the present crisis around the world. If we are not the advocates in the name of Christ, who will be?"
Welby told Francis that "there has come to many a new longing for the unity of all Christians."
"However, the journey is testing and we cannot be unaware that differences exist about how we bring the Christian faith to bear on the challenges thrown up by modern society," he added.
While both leaders stand firm on some social questions such as traditional family values, for example, Welby supports the ordination of women bishops.
But he said "recent decades, however, have been marked by a journey of rapprochement and fraternity, and for this we give heartfelt thanks to God."
"I am grateful, too, for the sincere efforts the Church of England has made to understand the reasons that led my Predecessor, Pope Benedict XVI, to provide a canonical structure able to respond to the wishes of those groups of Anglicans who have asked to be received collectively into the Catholic Church," Francis added.