Bishop Richard Williamson, with the conservative Society of St. Pius X, had faced worldwide criticism over a television interview in which he said no Jews were gassed during the Holocaust.
Last month, the pope sought to help heal a rift with ultra-traditionalists by lifting a 20-year-oldand three other bishops who had been consecrated without Vatican approval.
The move immediately caused an uproar among Jewish groups.and spoke out against anti-Semitism and Holocaust denial.
"Observing these consequences I can truthfully say that I regret having made such remarks," Williamson was quoted as saying in a statement carried by the Zenit Catholic news agency.
"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," Williamson added, according to Zenit.
The agency quoted him as saying that to all that took offense, "before God I apologize."
In the interview shown on Swedish state TV, Williamson said historical evidence indicates there were no Nazi gas chambers and that a maximum of 300,000 people died in concentration camps in the Holocaust.
Most historians believe about 6 million Jews died at the hands of the Nazis during the Holocaust.
Zenit said on its Web site that the statement was published upon Williamson's return to London on Wednesday. The bishop was expelled from Argentina, where he had been based, following the controversy.