Cardinal Keith O'Brien, who resigned last week as Britain's most senior Roman Catholic cleric, on Sunday admitted that his sexual conduct had "fallen below the standards expected of me".
A statement released by the former head of the Catholic Church in Scotland apologised "to those I have offended... to the Catholic Church and people of Scotland."
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.
O'Brien resigned as head of the Scottish church 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.
"To those I have offended, I apologise and ask forgiveness," he said in Sunday's statement. "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."
He confirmed in his resignation statement that he will not take part in the papal election conclave, which has been overshadowed by controversies surrounding O'Brien and other cardinals caught up in sex scandals.
He had been due to resign on his 75th birthday later this month but said on Monday that the pope had decided it should take effect immediately.
The allegations include claims that one priest received unwanted attention from O'Brien after a late-night drinking session, Britain's Observer newspaper reported last month.
Another priest reportedly claims that O'Brien used night prayers as cover for inappropriate contact.
In new claims published in Sunday's Observer, one of the claimants said he had been "disappointed" by the Church's response.
"There have been two sensations for me this week," he said. "One is feeling the hot breath of the media on the back of my neck and the other is sensing the cold disapproval of the Church hierarchy for daring to break ranks. I feel like if they could crush me, they would.
"The vacuum the Church has created has allowed whimsy and speculation to distort the truth, and the only support I have been offered is a cursory email with a couple of telephone numbers of counsellors hundreds of miles away from me," he added.
A string of new scandals and allegations have emerged since Benedict became only the second pope in the Church's 2,000-year history to step down of his own free will.
Four members of the conclave are associated with the paedophile priest scandals that have dominated Benedict's eight-year rule as pope.
And while 85-year-old Benedict cited his age as the main factor in his resignation, media have speculated that an explosive report into last year's "Vatileaks" scandal may have played a role.
O'Brien has previously angered the gay community with his hardline public stance on homosexuality. He was named "bigot of the year" last year by the gay rights charity Stonewall.
He recently said that same-sex marriages would be "harmful to the physical, mental and spiritual well-being of those involved" and has long voiced opposition to gay adoption.
But he has also called for priests to be able to marry and have children.
"Many priests have found it very difficult to cope with celibacy as they lived out their priesthood, and felt the need of a companion, of a woman, to whom they could get married and raise a family of their own," he told BBC television.