It also said Pope Benedict XVI had not known about Bishop Richard Williamson's views when he agreed to lift his excommunication and that of three other ultraconservative bishops Jan. 21.
The Vatican's Secretariat of State issued the statement a day after German Chancellor Angela Merkel urged the pope to make a clearer rejection of Holocaust denials, saying there had not been adequate clarification from the church.
The Holy See on Jan. 24 announced the rehabilitation of four bishops excommunicated in 1988 after being consecrated without papal consent.
Just days before, Williamson had been shown on Swedish state television saying historical evidence "is hugely against 6 million Jews having been deliberately gassed" during World War II.
Williamson has since apologized to the German-born pope for having stirred controversy, but he did not repudiate his comments, in which he also said only 200,000 to 300,000 Jews were killed during World War II and none were gassed.
Though the Vatican said it did not share Williamson's views, Jewish groups voiced outrage at his rehabilitation and demanded the prelate recant.
Williamson and the three other bishops were consecrated by the late ultraconservative Archbishop Marcel Lefebvre, who in 1969 founded the traditionalist Society of St. Pius X opposed to the liberalizing reforms of the Second Vatican Council, including its outreach to Jews.
The Vatican said Wednesday that, while Williamson's excommunication had been lifted, he still had no canonical function in the church because he was consecrated illegitimately.
"Bishop Williamson, in order to be admitted to episcopal functions within the church, will have to take his distance, in an absolutely unequivocal and public fashion, from his position on the Shoah, which the Holy Father was not aware of when the excommunication was lifted," the statement said. The Shoah is the Hebrew term for the Holocaust.
Jewish groups welcomed the Vatican statement, saying it satisfied their key demand.
"This was the sign the Jewish world has been waiting for," said Ronald Lauder, president of the World Jewish Congress.
Elan Steinberg, vice president of the American Gathering of Holocaust Survivors and their Descendants, thanked Merkel for her "righteous comments" and said the process to heal the "deep wound that this crisis caused to the Catholic-Jewish dialogue" could now begin.
Williamson's interview on Swedish state TV was aired Jan. 21. The decree lifting his excommunication bore the same date, although it was not announced until three days later. The broadcaster said the timing was a coincidence, but Williamson has expressed his views about the Holocaust previously.
Wednesday's statement was a remarkable turnabout by the Vatican, which had considered the Williamson case "closed" after Benedict issued a lengthy denunciation of Holocaust deniers last week and the society itself distanced itself from Williamson's views.
On Jan. 28, the pope said he felt "full and indisputable solidarity" with Jews, and warned against any denial of the full horror of the Nazi genocide.
The Vatican's secretary of state, Cardinal Tarcisio Bertone, cited those comments Tuesday in telling the newspaper of the Italian bishops' conference Avvenire that, as far as he was concerned, "the question can be considered closed."
Yet the pressure continued, including from Roman Catholic leaders in Benedict's native Germany and Merkel's comments Tuesday.
It was not immediately clear if the Vatican's newest statement Wednesday satisfied Merkel.
"The chancellor has spoken and has nothing to add to her comments from yesterday," her spokesman Ulrich Wilhelm told reporters in Berlin.
In addition to its demand of Williamson, the Vatican also said society as a whole must fully recognize the teachings of Vatican II and of all popes who came during and after it in order to have a legitimate canonical function in the church.
There was no answer to several calls placed Wednesday to Williamson's home in La Reya, Argentina.