Bishop Richard Williamson apologised to all those he offended with his Holocaust-denying remarks, in a letter to the Vatican.
‘Observing these consequences I can truthfully say that I regret having made such remarks,’ said Bishop Williamson in the letter made public a day after his return to Britain from Argentina.
‘If I had known beforehand the full harm and hurt to which they would give rise, especially to the Church, but also to survivors and relatives of victims of injustice under the Third Reich, I would not have made them,’ he said.
‘To all souls that took honest scandal from what I said, before God I apologise," he wrote.
‘As the Holy Father has said, every act of unjust violence against one man hurts all mankind.’
The letter was written from London.
Vatican spokesman Federico Lombardi, however, said he had not yet been informed of it.
Bishop Williamson, aged 68, indicated in the letter that he was responding to a demand by the pope to reconsider his comments.
The bishop has been at the centre of a raging controversy after saying on Swedish television last month: ‘There was not one Jew killed by the gas chambers. It was all lies, lies, lies.’
Williamson said he believed ‘200,000 to 300,000 Jews perished in Nazi concentration camps, but none of them by gas chambers.’
He was among four bishops that Pope Benedict XVI agreed to take back in January in an attempt by the Vatican to heal a split with traditionalist Roman Catholics who rejected the church's liberal reforms of the early 1960s.
Until now, Bishop Williamson had refused to withdraw his claims, despite Vatican demands for him to unequivocally distance himself from his statements.