The director of the mayor’s new Office for the Prevention of Hate Crimes is alreadydisagreeing with her new boss — who claimed in June that anti-Semitism is a right-wing movement.

“He’s correct to say there are threats that come from the right wing. There are also threats that come from the left,” said Deborah Lauter at a City Hall press conference Tuesday announcing her new position. Oddly, de Blasio did not attend the event.

“I don’t know the mayor’s schedule but I can assure you that everything that’s been communicated to me is the mayor’s taking this extremely seriously,” Lauter said when asked why de Blasio was a no-show. She also hasn’t met with the mayor since taking the job last week.

Lauter, who worked at the Anti-Defamation League for 18 years before taking the city position, said she was “not aware” of a right-wing threat of anti-Semitism in New York.

At a June press conference addressing a 90 percent spike in anti-Jewish incidents in the city, de Blasio said that “the ideological movement that is anti-Semitic is the right-wing movement.” At the same event, NYPD Chief Dermot Shea said perpetrators of hate crimes include teens, people with mental illness, first-time offenders and career criminals.

Lauter’s office will have five to six staff. She did not have details about its budget.

She revealed at the press conference that her family was the victim of a hate crime when she served as a regional director for the Anti-Defamation League in Atlanta in the 1990s.

Lauter, who is Jewish and had experienced online epithets from the Ku Klux Klan, found pork and shellfish products in her mailbox one day. Jews who keep a kosher diet do not eat pork or shellfish.

“When it happened to me personally, I realized how much it meant to my identity and how much fear it raised,” she said.