Cardinal Basil Hume, leader of the Catholic Church in Britain, is said to be privately "contemptuous" of his opposite number in the Church of England, Dr George Carey.
The allegation is made by Tory MP Ms Anne Widdecombe in a new book, entitled Basil Hume: By His Friends, and seems to have set in motion strenuous efforts on both sides to defuse any potential dispute.
Cardinal Hume has reportedly written to Dr Carey, saying: "We must not let others drive wedges between us. I am particularly sorry about this because I have always valued your friendship and kindness towards me."
Dr Carey is said to have sent replies in a similar vein.
Ms Widdecombe, an Anglican who converted to Catholicism after the Church of England decided to ordain women priests in November 1992, is one of 24 people to contribute to the book, serialised in the Times of London.
In it she describes Cardinal Hume as "cross and crusty, gentle and endearing, tough and uncompromising, sensitive and diplomatic. He hates rows."
She went on: "Those who know him say his attitude to George Carey, the Archbishop of Canterbury, verges on the contemptuous in private, but no trace of this has ever been publicly discernible." She added that relations between the two denominations "appear to have weathered the storm" following defections from the Church of England.