Livingstone has previously called Prime Minister Ariel Sharon a war criminal and said he should be imprisoned with former Serbian ruler Slobodan Milosevic.
At a weekly press conference Livingstone said he had nothing to apologize about.
He said he has been through many media storms in his time and whenever he felt it necessary to apologize, he did.
“But I will not apologize as I don’t believe I did anything wrong," he said.
He added that he plans to send a letter to the city council giving his version of the incident.
“You can think that my remarks are offensive, …If you think my remarks are racist I think you are wrong,” he said. “It would be very easy for me to buy off media pressure by lying but I’m not going to do that.”
Mayor could face 5-year suspension
Earlier, Livingstone had rejected calls by Jewish organizations, council members, and Labor party colleagues to issue an apology.
“I will not say things I do not believe in,” he said.
The controversy was stirred up over the weekend in the U.K. when Oliver Feingold, a Jewish reporter from the Evening Standard covered a party attended by Livingstone.
According to Feingold, he had asked the mayor an innocent question and was answered rudely. In footage from the event the mayor is heard saying: “ Are you a Nazi war criminal?”
Feingold, who was shocked, immediately made it clear that he was Jewish and that he found the remark offensive.
Livingstone responded by saying Feingold may be Jewish, but he was just like a Nazi camp guard doing his job because he was being paid to do it.
The remarks came amid a long-term dispute between Livingstone and the Evening Standard and Daily Mirror papers. Livingston said the publications had been running a long-term hate campaign against him and his family for more than 24 years.
Livingston’s refusal to apologize for his remarks led Jewish leaders in the U.K to file an official complaint against him.
A decision as to whether a formal investigation will be launched is expected to be made within 10 days. Should Livingstone be found to have acted inappropriately, he would be removed from public office for five years.