The Anti-Defamation League and the Anne Frank Center for Mutual Respect condemned Trump for what they characterised as trivialising one of the singular horrors of the 20th century to score a political point, The New York Times reported.
"Has he no sense of shame?" Steven Goldstein, executive director of the Anne Frank Center for Mutual Respect, said.
The Center is the American chapter of an international group that fights prejudice to honor the legacy of Anne Frank, the teenage diarist who perished in the Holocaust in 1945.
"Either he is completely callous in attacking US intelligence, or he is so ignorant of history that you would never want this man to be president."
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Jonathan A Greenblatt, the chief executive of the Anti- Defamation League, said that Trump's analogy was "not only an inappropriate comparison on the merits, but it also coarsens our discourse."
Asserting that no one should cavalierly draw analogies to Nazi Germany, Greenblatt said it would be helpful for Trump to explain his intentions or apologise for the remark.
"Intelligence agencies should never have allowed this fake news to 'leak into the public. One last shot at me. Are we living in Nazi Germany?" he tweeted yesterday.
The American Jewish Committee tweeted back: "We regret @realDonaldTrump's use of Nazi Germany regarding the media - an inappropriate comparison that diminishes the horrors of that time."
This is not the first time Trump has gotten into trouble with Jewish groups while making a political point.