Livingstone is reported to have known the reporter, Oliver Finegold, 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".
Livingstone is not the first to make fascist jibes at Associated Newspapers. In September 2003, Richard Desmond published a story in the Sunday Express detailing links between Associated Newspapers proprietor Lord Rothermere and the Nazis. The Sunday Express claimed that Adolf Hitler had written a letter to the late Daily Mail boss Lord Rothermere calling him his "sincerest friend".
Livingstone has had previous run-ins with the Evening Standard, where he has described it damningly as a "pale imitation of the Daily Mail" and said that it is out of touch with readers.
According to reports, the incident began after the reporter introduced himself and asked for a comment from the Mayor.
Livingstone replied: "How awful for you. Have you thought of having treatment?"
A spokesman for the Mayor hit out at the Standard for attending an event that was largely a lesbian and gay event. The exchange is said to have reached the point where the reporter told the Mayor to "fuck off".
A spokesman for the Mayor said: "In these circumstances, it is hardly surprising that the discussion between the journalist and the Mayor escalated from relatively light-hearted comments of the Mayor asking whether the journalist’s previous job had been as a war criminal -- given the paper he was working for -- to the journalist eventually telling the mayor to 'fuck off'."
The Evening Standard has declined to comment on the incident.
The row between the reporter and the Mayor follows an ongoing war of words between the paper and its owners Associated Newspapers.
Last month, Livingstone opened the way for Richard Desmond to launch his long-planned London freesheet rival to Associated Newspapers' Metro. The move could be disastrous for the Evening Standard as more of its circulation is eaten away.
Livingstone said that the exclusive distribution deal with Metro did not allow Londoners to get the benefit of a free afternoon paper.
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