Calls for Livingstone to apologise for his racial slur, following an argument with the reporter Oliver Finegold, came from prominent individuals and groups within the Jewish community.
Livingstone is reported to have known the reporter was Jewish before he made his comments, which closely follows Holocaust Memorial Day.
The two exchanged words following a party marking the 20-year anniversary since Labour MP Chris Smith, who recently revealed he was HIV positive, became the first MP to come out as gay.
Livingstone is further said to have told the reporter that he should work for a paper "that doesn't have a record of supporting fascism". The comment was a reference to the Standard's sister paper, the Daily Mail, which in 1934 ran a front page story declaring "Hurrah for the Blackshirts".
The Evening Standard, which has splashed the story on its front page morning edition quoted Auschwitz, Buchenwald and Bergen-Belsen death camp survivor Gina Turgel MBE as saying "perhaps the Mayor does not understand the pain we went through".
Henry Grunwald, president of the Board of Deputies of British Jews, told the paper that Livingstone should consider his position.
"These words are appalling. His insensitivity seems to know no bounds. He should consider his position as Mayor of this great city," Grunwald said.
A spokesman for the Jewish Protection Agency said Livingstone should apologise to not only the Jewish community and Finegold, but to the editor of the Evening Standard.
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