Cardinal Keith O'Brien has admitted that his sexual conduct had at times "fallen below the standards expected of me as a priest, archbishop and cardinal".
The cardinal, who was Britain's most senior Catholic cleric, stepped down from his post as Archbishop of St Andrews and Edinburgh last week, a day after three priests and a former priest made allegations of "inappropriate" behaviour against him.
In a statement issued by the Catholic Church in Scotland, he apologised and asked forgiveness from those he had "offended".
"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," the statement said.
Cardinal O'Brien said he will spend the rest of his life in retirement and will play no further part in the public life of the Catholic Church in Scotland.