"To those whom I have offended, I apologise and ask forgiveness," Cardinal Keith O'Brien said in a statement.
Cardinal Keith O'Brien, until last week Britain's most senior Catholic clergyman, has admitted to sexual conduct that fell "beneath the standards expected of me".
One week after denying allegations by other priests that he made "inappropriate advances" stretching back 30 years, O'Brien issued a statement apologising and asking the forgiveness of those he had "offended".
He also apologised to the Catholic Church, and to the people of Scotland.
He resigned last week after three priests and one former priest made allegations of improper behaviour against him in the Observer newspaper.
In his statement today, issued through the Roman Catholic Church in Scotland, O'Brien said: "In recent days certain allegations which have been made against me have become public. Initially, their anonymous and non-specific nature led me to contest them.
"However, I wish to take this opportunity to admit that there have been times that my sexual conduct has fallen below the standards expected of me as a priest, archbishop and cardinal.
"To those I have offended, I apologise and ask forgiveness. To the Catholic Church and people of Scotland, I also apologise.
"I will now spend the rest of my life in retirement. I will play no further part in the public life of the Catholic Church in Scotland."
O'Brien was Britain's most senior Roman Catholic cleric when he resigned last Monday as the Archbishop of St Andrew's and Edinburgh, and said he would not take part in the election for a successor to Pope Benedict.
He had been due to retire later this month when he turned 75.
Religious commentator Steven Bates said: "It's a great personal humilation, a real unravelling of the hierarchy of the Scottish Catholic Church."
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