Speaking at the end of a week in which he was suspended from the Labour Party over comments judged to have been anti-Semitic, Livingstone said he was "not going to apologise for telling the truth".
He did say he regretted mentioning Adolf Hitler in an interview and the disruption his comments had caused.
Earlier this week, defending MP Naz Shah, who was suspended from the party after herself being accused of anti-Semitism, he told LBC:
She’s a deep critic of Israel and its policies. Her remarks were over the top but she’s not anti-Semitic. I’ve been in the Labour party for 47 years; I’ve never heard anyone say anything anti-Semitic.
Let’s remember when Hitler won his election … his policy was that Jews should be moved to Israel. He was supporting Zionism.
Livingstone was later accused by a Labour MP of being a "Nazi apologist" and suspended from the party.
Speaking again to LBC today, Livingstone declined the opportunity to apologise for his comments.
"I never regret saying something that is true," he said. "How can I have hurt and offended the Jewish community when the prime minister of Israel said exactly the same thing?"
Livingstone's LBC interviewer suggested the Jewish vote for Labour would be “much depleted” in the London mayoral election next week.
Livingstone said: “No, I think they're going to come out and vote for the Labour candidate because he's been absolutely clear, he's denounced anti-Semitism.”
He added: “The simple fact in all of this is I did not create this problem, it was created by a group of embittered Blairite MPs.”
Full story: No apology from Ken Livingstone: City A.M.