A man chosen by GOP presidential candidate Donald Trump as one of his foreign policy advisers has reportedly questioned the Holocaust, saying the ovens were "too small" to kill so many Jews.

Former Department of Defence inspector general, Joseph Schmitz, is also accused of bragging about firing Jewish staffers as an "achievement" during his time at the Pentagon from 2002 to 2005, according to a federal employee complaint obtained by the Washington bureau of the McClatchy newspapers.

In the complaint, senior Pentagon officer Daniel Meyer said that Schmitz boasted about firing Jews, and "lectured" another official about "details of concentration camps and how the ovens were too small to kill 6 million Jews," McClatchy reported.

Schmitz denied the claims, calling them "preposterously false and defamatory," and noting that he has a Jewish wife. He then clarified to McClatchy that his wife was "ethnically" Jewish and not a practising Jew.

However, a lawyer for another employee – army engineer David Tannenbaum at the Tank Automotive Command in Michigan – wrote a letter this week to the Pentagon's acting inspector general, blaming Schmitz for creating an "anti-Semitic culture" within the military.

Trump named Schmitz as one of five foreign policy advisers in March. Schmitz has said he helped write one of Trump's foreign policy speeches and that Trump consults him regularly.

It is not the first time the Trump campaign has been tainted by accusations of anti-Semitism. Trump came under fire in December 2015 after he told a Republican Jewish Coalition in December: "I'm a negotiator, like you folks."

In July 2016, the campaign posted a tweet, calling opponent Hillary Clinton the "most corrupt candidate ever," and used an image pulled from a white supremacist message board. The image featured Clinton next to a pile of money and six-pointed star that many viewed as the Jewish Star of David. Former grand wizard of the Ku Klux Klan, David Duke, praised the Tweet.

Trump insisted it was a sheriff's star but quickly changed it to a circle following a barrage of criticism. He later said he was sorry he caved into pressure.

Trump's Jewish son-in-law Jared Kushner – the husband of Ivanka, who has converted to Judaism – defended Trump against charges of anti-Semitism after the star controversy.

But one of his employees at the New York Observer wrote an open letter to her boss saying: "Please do not condescend to me and pretend you don't understand the imagery of a six-sided star when juxtaposed with money and accusations of financial dishonesty."

There was no immediate response to the Schmitz report from the Trump campaign.