The Most Reverend Justin Welby was visiting Cornwall as part of his journey of prayer.
The leader of America's two million Episcopalians, the Most Reverend Katharine Jefferts Schori, also welcomed the move.
The current archbishop, the Most Reverend Rowan Williams, retires next month after 10 years in the role.
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Senator Sir Philip Bailhache wrote to the Most Reverend Justin Welby questioning the fairness of the review.
The Archbishop of Birmingham, The Most Reverend Bernard Longley, sent his condolences in a message from Rome.
The resignation of the Archbishop of Liverpool, the Most Reverend Patrick Kelly, has been formally accepted by the Pope.
The Archbishop of Liverpool, the Most Reverend Patrick Kelly, will not be celebrating Midnight Mass following his stroke on Monday.
But the Most Reverend Justin Welby told the BBC business morality was in many ways much better than in the past.
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The Archbishop of Liverpool, the Most Reverend Patrick Kelly, who suffered a slight stroke recently, has said he plans to retire.
The Most Reverend Rowan Williams told the ruling general synod that the Church could be seen as "wilfully blind" to modern trends and priorities.
BBC: Women bishops: Church has 'lost credibility' says Rowan Williams - BBC News
At a press conference in Cardiff, his replacement, the Most Reverend Archbishop- Elect said he was mindful of problems in the archdiocese.
The Most Reverend Rowan Williams said he was delighted by the appointment.
The leader of Roman Catholics in England and Wales, the Most Reverend Vincent Nichols, said the Pope's visit had been "better than he expected".
His successor, the Most Reverend Justin Welby, was enthroned in March.
The Archbishop of Liverpool the Most Reverend Patrick Kelly, who announced his own retirement this month after suffering a stroke, has paid tribute to the Bishop.
The most reverend prelate, Dr Rowan Williams, continued: "At the present moment the position of Christians in the region is more vulnerable than it has been for centuries".
The Archbishop of Canterbury the Most Reverend Justin Welby, who has in the past praised the quality of same-sex relationships, sees the Church's response to the issue as a challenge.
The Archbishop of Canterbury, the Most Reverend Rowan Williams, his soon-to-be successor the Bishop of Durham, the Right Reverend Justin Welby, and the Archbishop of York, Dr John Sentamu will be tweeting.
The next Archbishop of Canterbury, Rt Rev Justin Welby, has called the rejection a "very grim day", and the retiring Archbiship - the Most Reverend Rowan Williams - said the church had lost "credibility".
In 2006 the Episcopalian Church in the United States became the first province of the Anglican Communion to elect a woman to the role of Primate (a senior bishop - the equivalent of an archbishop) - the Most Reverend Katharine Jefferts Schori.
Archbishop Robin Eames of the Church of Ireland and, perhaps most significantly, the Reverend William Bingham, a leading Orangeman, were also shocked into action.
One of Mr Mutharika's most bitter critics, the Reverend Daniel Gunya says church leaders campaigned against Mr Mutharika because they did not want Mr Muluzi's legacy to continue.
The industrial revolution gave us the Reverend Thomas Malthus, that most fearful of latter-day apocalyptics.
The Reverend Ron Williams, in his Christmas message, said the fact that most people in Wales ticked the "Christian" box was a "source of optimism".
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The fact that so many people are surprised to hear that anger in some of Reverend Wright's sermons simply reminds us of the old truism that the most segregated hour of American life occurs on Sunday morning.
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