Vatican spokesman the Rev. Federico Lombardi said Friday that Bishop Richard Williamson's statement "does not seem to respect the conditions" the Vatican set out for him.
Williamson. But he did not say his comments had been erroneous, or that he no longer believed them.
He had denied 6 million Jews were killed during the Holocaust, and maintained that no Jew was gassed.
The Vatican on Feb. 4 said Williamson must "absolutely and unequivocally distance himself" from his remarks if he wants to be admitted as a prelate in the church.
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 immediatelyamong 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.