Dr Christopher Collingwood claims the eastern practise of Zen resonates with Christian contemplation and described himself in an article by the Daily Telegraph as "religiously bilingual", following aspects of both beliefs.
He established the Zen Sangha two-years-ago, a group which holds fortnightly half-hourly meditation sessions at the Minster's Library building in Dean's Park, the Old Palace.
Dr Christopher is quoted in the Daily Telegraph as saying: "When people are meditating in Zen who are Christian I think the focussing on the breath coincides with the idea of the Holy Spirit.
"I'm sure there are those who think I'm an out and out heretic but it seems to me perhaps Zen poses fewer problems [than other non-Christian customs] because it doesn't claim to be a system of doctrine or belief."
Speaking with Premier, Andrea Williams, Chief Executive of Christian Concern said the two practises were incompatible and called on Dr Christopher to resign.
Andrea Williams also said: "Buddhism contrasts sharply with Christian teaching about God. The two are incompatible. To try to mix them is deceptive and dishonours Jesus Christ.
"It is remarkable that this is happening at one of the country's best known cathedrals. The Archbishop of York must take swift action. This type of confusion undermines the Church of England's current initiative to encourage Christian prayer.
"Unless there is clarity about the Christian gospel at the heart of the Church of England's call to prayer, the initiative will be counter-productive.
In a statement, the Very Reverend Vivienne Faull, Dean of York said: "The Zen group is not a religious order of any kind and the Chapter of York would not give permission for any such religious order to be set up at York Minster.
"The meetings aim to offer an opportunity for Christians and others to come together to learn about and explore Zen meditation practices and the congruence of Zen with Christian faith."
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