A senior White House official, Sebastian Gorka, has been linked to a Hungarian nationalist group that once collaborated with the Nazis. And that has some U.S. Jewish groups concerned.

The Jewish Daily Forward on Thursday reported that multiple leaders of an offshoot of the far-right Vitezi Rend (“Order of Heroes”) in Hungary claim that Gorka is a sworn member, as was his father. Gorka, 46, later immigrated to the United States and became a naturalized citizen in 2012.

Last month, journalists noted that Gorka has worn a medal affiliated with the group in public on multiple occasions, and that he has further ties to anti-Semitic groups in Hungary. Gorka said he wears the medal as a tribute to his father.

Centrist and left-leaning Jewish organizations including J Street, the Anti-Defamation League, and the Anne Frank Center have all released critical statements on Gorka’s reported links to Vitezi Rend. “If true, he needs to renounce his membership immediately and disavow their exclusionary message of hate,” said Anti-Defamation League director Jonathan Greenblatt in a statement.

And yet other Jewish organizations inclined to support Trump have either praised Gorka as a hardcore pro-Israel figure, or shied away from commenting altogether. The right-wing Zionist Organization of America (which defended Steve Bannon over a different anti-Semitism flap earlier this year) released a statement saying “Gorka is a friend of Jews/Israel.”

Allen Fagin, executive vp of the Trump-friendly Orthodox Union, the largest organizational body for Orthodox Jewish synagogues in the country, said, “It’s something we probably want to find out more about.”

But Fagin also noted that “there are serious people within the community that I’m aware of who have said very, very positive things about Dr. Gorka.”

A spokesperson for the Republican Jewish Coalition did not respond to multiple requests for comment. Nor did Malcolm Hoenlein, executive vice chairman of the Conference of Presidents of Major American Jewish Organizations and a right-leaning power broker who is well-known within the American-Jewish establishment.

Vitezi Rend is a Hungarian nationalist group founded in the 1920s by Admiral Miklos Horthy, the ruler of Hungary who helped send Hungarian Jews en masse to Auschwitz during the Holocaust. Today, the group is more of a cultural and historical organization — the offshoot that claims Gorka as a member is formally called the “Historical Vitezi Rend” — than a politically active group. The State Department designated the group a criminal organization because earlier members of the group collaborated with the Nazi regime.

Gorka denied these claims in the Forward story in an interview with the Jewish publication Tablet, although he didn’t issue a concrete denial about his alleged Vitezi Rend membership in a subsequent comment given directly to the Forward.

And yet Vitezi Rend official Kornel Pinter told the Forward that Gorka is a member. “Of course he was sworn in,” Pinter said, adding that he once met Gorka and his father in a city near the Hungarian-Austrian border.

Gorka did not respond to repeated requests for comment sent to a personal email address. White House spokesperson Sarah Huckabee Sanders directed VICE News to “two stories that more accurately portray Mr. Gorka” in the Jerusalem Post and PJMedia.com.

Neither story refutes the Vitezi Rend allegations, but both defend Gorka’s record as an ardent supporter of the state of Israel, with the Post describing him as a “philo-Semite.”

Ferenc Raj, rabbi emeritus of Congregation Beth El in Berkeley, California, who holds a doctorate in Near Eastern and Judaic Studies from Brandeis University (and who fled to the U.S. from Hungary in 1972), told VICE News in an interview that he is “puzzled.”