Speaking on Tuesday, the famously outspoken left-wing politician countered claims that the row could harm London's bid for the 2012 Olympics.
He said at one point that his remarks were "offensive but not racist" and thus did not require an apology.
If being rude to journalists were to be made a criminal offence, Livingstone joked, he would have committed "about 300 offences" over the past two decades.
Despite his defiant attitude, Livingstone has been under increasing pressure to apologise, something demanded by The Board of Deputies of British Jews as well as some Holocaust survivors.
The furore erupted last week when Livingstone was approached at a public function by a reporter from the London Evening Standard newspaper, with which the mayor has long had a mutually hostile relationship.
According to a tape transcript released by the paper, Livingstone first asked reporter Oliver Finegold if he was a "German war criminal", a reference to support offered in the 1930s to the British Union of Fascists by the Standard's sister paper, the Daily Mail.
When Finegold said he was Jewish and was offended by the comment, Livingstone responded by saying the reporter was "just like a concentration camp guard" and should not work for a title with "a record of supporting fascism".
Reason for comments
The mayor is waiting to see whether local government watchdog, the Standards Board for England, will launch an investigation which could see him suspended from office.
He said there had been a serious purpose to his comments.
"It is the thin end of the wedge when reporters say to me: 'I'm only doing this because this is my job'," he said.
"That is the same abdication of moral responsibility, the thin edge of the wedge that in its extreme horrific version that ends up being compared to standing around like a concentration camp guard. You are responsible for your own choices in life."
Opposition politicians have urged the mayor to back down, saying the row is hurting London's Olympic chances, with inspectors from the International Olympic Committee currently in London.
"This row has done incalculable damage to his reputation, to his long-term position as mayor - and to London's Olympic bid," Bob Neill, leader of the London Assembly Conservatives, said.