VATICAN CITY - An apology from a bishop who denied the Holocaust wasn't good enough, the Vatican said Friday, adding that he must repudiate his views if he wants to be a Roman Catholic clergyman.

The statement by Bishop Richard Williamson "doesn't appear to respect the conditions" the Vatican set out for him, said Rev. Federico Lombardi, a spokesman for the Pope.

In an interview broadcast last month on Swedish state TV and in previous letters and speeches, Williamson denied six million Jews were killed in the Holocaust, saying about 200,000 or 300,000 were murdered. He said none was gassed.

Williamson apologized for his remarks on Thursday upon his arrival in his native Britain after being ordered to leave Argentina. He said he would never have made them if he had known "the full harm and hurt to which they would give rise."

But he didn't say he had been wrong or that he no longer believed what he had said.

On Friday, German Justice Minister Brigitte Zypries said Germany could issue a European-wide arrest warrant on hate crimes charges for Williamson since the Swedish TV interview was conducted in Germany.

State prosecutors in Regensburg, Germany, have opened a preliminary investigation into whether Williamson broke German laws against Holocaust denial.

His remarks prompted widespread outrage among Jewish groups and others. They also embarrassed the Vatican since they were broadcast just days before the Holy See announced it was lifting Williamson's excommunication and that of three other bishops.

The four, members of the traditionalist Society of St. Pius X, had been excommunicated after being consecrated as bishops without papal consent in 1988.

Bowing to the criticism, the Vatican on Feb. 4 demanded that Williamson "absolutely and unequivocally distance himself from his remarks about the Shoah if he is to be admitted to episcopal functions in the church." Shoah is the Hebrew term for the Holocaust.

The German-born Pope Benedict also met with Jewish leaders at the Vatican and told them it was unacceptable for anyone -- particularly a clergyman -- to deny or minimize the Holocaust.

In his statement Friday, Lombardi noted that Williamson's comments were not addressed to the pontiff or to the Vatican's Ecclesia Dei commission, which has been dealing with the Society of St. Pius X ever since its bishops were excommunicated.

Rather, Williamson issued a statement that was carried by the Zenit Catholic news agency and posted on the society's British website and its news agency, www.dici.org.

In it, Williamson said he was only giving the opinion of a "non-historian" during the Swedish TV interview. He said that opinion was "formed 20 years ago on the basis of evidence then available, and rarely expressed in public since."

"To all souls that took honest scandal from what I said, before God I apologize."

Jewish groups were not impressed.

"This is another sham statement that doesn't recant any of his earlier remarks about the Holocaust," said Abraham Foxman, ADL National Director and a Holocaust survivor. "Bishop Williamson must unequivocally acknowledge the full extent of the Holocaust and recognize the fact of the existence of the gas chambers."

The American Jewish Congress praised the Vatican for demanding more.

"Until he explicitly says otherwise, he remains in the camp of the Holocaust deniers," said AJC executive director David Harris. "He is not fooling anyone, least of all the Vatican."

The Society of St. Pius X has distanced itself from Williamson's remarks and removed him as the director of its seminary in La Reja, Argentina.

The Switzerland-based society was formed in 1969 by the late Archbishop Marcel Lefebvre, opposed to the liberalizing reforms of the Second Vatican Council, particularly its outreach to Jews.

While Williamson was readmitted as a baptized Catholic back into the church when the excommunication was lifted, he still has no standing in the church as a bishop, said Rev. John Coughlin, professor of canon law at the University of Notre Dame Law School.

That is because the church considers that his consecration was "valid but illicit."

It was valid because Lefebvre was a validly ordained bishop in the Catholic Church, and thus could validly ordain others. But because Lefebvre had been suspended in 1976, he had no authority from the Pope to consecrate bishops, meaning their consecrations were illicit, or illegal in the church's eyes, he said.

Williamson will only be able to function legally as a bishop in the Catholic Church once he has received a mandate from the Pope, Coughlin said.