French Jews accused a left-wing presidential candidate of encouraging Holocaust denial following his comparison of the Nazi persecution of Jews to the situation of French Muslims today.

Vincent Peillon, who is running in the Socialist Party primaries ahead of the elections this year, made the analogy Tuesday during an interview aired by the France 2 television channel.

Peillon, a former education minister who has Jewish origins, was commenting on a question about France’s strict separation between state and religion, referred to in France as “laicite.”

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“If some want to use laicite, as has been done in the past, against certain populations … Forty years ago it was the Jews who put on yellow stars. Today, some of our Muslim countrymen are often portrayed as radical Islamists. It is intolerable.”

In a statement Wednesday, CRIF, the umbrella group of French Jewish communities, accused Peillon of making “statements that only serve those trying to rewrite history.”

Peillon neither retracted his remark nor apologized in a statement published Wednesday on his website, but said he would wanted to elaborate on what he meant in light of the controversy it provoked and to “refine my view, which may have been misrepresented because of brevity.”

Peillon wrote that he “clearly did not want to say that laicite was the origin of anti-Semitism of Vichy France,” which was the part of the country run by a pro-Nazi collaborationist government. He also wrote that “what the Jews experienced under Vichy should not be banalized in any way” and that he was committed to fighting racism and anti-Semitism.

“I wanted to denounce the strategy of the far right, which always used the words of the French Republic or social issues to turn them against the population. It is doing so today with laicite against the Muslims,” Peillon wrote.

But in its statement condemning Peillon’s remark, CRIF wrote that the history concerning the deportation of more than 75,000 Jews from France to concentration camps and death and the looting of their property, “as well as discriminatory laws such as the one about wearing yellow stars, should not be instrumentalized to create a false equivalence of suffering.”

CRIF “demands a clarification and immediate correction on the part of Vincent Peillon,” it said.

Peillon, a lawmaker in the European Parliament, announced his candidacy in December to succeed President Francois Hollande as party leader and run as its candidate in April. He was appointed education minister in 2012 and served for two years.

In the Socialist primaries, Peillon will face Prime Minister Manuel Valls, who has strong support in the Jewish community. Peillon’s mother, Françoise Blum, is Jewish.

Peillon, who rarely talks about his Jewish roots publicly, signed a petition by the left-wing Jcall group, the European counterpart to J Street, supporting Palestinian statehood.

In 2009, he celebrated the bar mitzvah of his son Elie at a Paris synagogue. He has another son, Isaac. Peillon is married to Nathalie Bensahel, a journalist who has written about France’s anti-Semitism problem.

Peillon opposed the ban last summer on women wearing the burkini, the full-body swimsuit favored by some Muslims, on public beaches. Valls supported the ban, citing what he said was its use by radical Muslims to oppress women.