Keith O'Brien, who resigned last week as Britain's most senior Roman Catholic cleric after claims of sexual impropriety, admitted on Sunday that his conduct had "fallen below the standards expected of me".
In a statement, O'Brien also apologised "to those I have offended... to the Catholic Church and people of Scotland."
O'Brien resigned as head of the Catholic Church in Scotland on Monday in the wake of claims that he made sexual advances towards priests.
"In recent days certain allegations which have been made against me have become public," said the cleric. "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," he added.
O'Brien -- who steps down as Archbishop of St Andrews and Edinburgh -- initially denied the allegations, which date back to the 1980s.
The 74-year-old had been due to be the only British cardinal to vote on a replacement for Pope Benedict XVI following the pontiff's shock resignation on February 11.
But O'Brien confirmed in his resignation statement that he will not take part in the election conclave, which has been overshadowed by controversies surrounding O'Brien and other cardinals caught up in sex scandals.