VATICAN CITY (Reuters) - The Vatican said on Friday that an apology by a traditionalist bishop who denied the Holocaust fell short of meeting the Holy See's demand for a full and public recanting of his position.

British Bishop Richard Williamson, whose comments in January caused a worldwide uproar among Jews and Catholics, on Thursday issued a statement in which he said: To all souls that took honest scandal from what I said, before God I apologize.

But chief Vatican spokesman Father Federico Lombardi said Williamson's statement does not seem to respect the conditions set forth by the Vatican on February 4, when it ordered Williamson to in an absolutely unequivocal and public way distance himself from his positions regarding the Holocaust.

On January 24, Pope Benedict lifted the excommunications of Williamson and three other bishops to try to heal a 20-year-old schism that began when they were thrown out of the Church for being ordained without the permission of Pope John Paul II.

Among those who condemned Williamson and the pope's decision were Holocaust survivors, progressive Catholics, members of the U.S. Congress, Israel's Chief Rabbinate, German Jewish leaders and Jewish writer and Nobel Peace Prize winner Elie Wiesel.

Williamson told Swedish television in an interview broadcast on January 21: I believe there were no gas chambers. He said no more than 300,000 Jews perished in Nazi concentration camps, rather than the 6 million accepted by mainstream historians.

In his statement issued on Thursday, Williamson said: I can truthfully say that I regret having made such remarks, and that 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 arrived in Britain earlier this week after he was ordered to leave Argentina, where he was the director of a seminary of the ultra-traditionalist Society of St. Pius X


(Editing by Jon Boyle)