Ken Livingstone has stood by his recent comments about Hitler, saying he is "not sorry for telling the truth".
He said he "regretted" the disruption his comments had caused but "I believe what I said is true".
The former London mayor was suspended from the Labour party on Thursday after saying Hitler had supported Zionism in the 1930s.
He made the comments while defending Labour MP Naz Shah over accusations she was anti-Semitic.
During an interview on LBC, Mr Livingstone repeatedly refused to apologise for making the comments, saying he was sorry if his views had upset Jewish people but he had simply made a "statement of fact" that had also been made by Israeli prime minister Benjamin Netanyahu.
"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?"
"If you look at what this is all about, it's not about anti-Semitism in the Labour Party... What this is all about is actually the struggle of the embittered old Blairite MPs to try to get rid of Jeremy Corbyn."
Labour is to hold an independent inquiry into anti-Semitism and other forms of racism in its ranks.
It said the inquiry, led by Shami Chakrabarti, former head of human rights campaign group Liberty, would consult with the Jewish community and other minority groups, after claims a strain of party members held anti-Semitic views.
The row erupted after Ms Shah was found to have made comments on Facebook before becoming an MP, including a suggestion that Israel should be moved to the United States. She later apologised and was suspended from the party.
But Mr Livingstone defended the Bradford West MP, saying anti-Zionism was not the same as anti-Semitism.
He told BBC London: "When Hitler won his election in 1932, his policy then was that Jews should be moved to Israel. He was supporting Zionism before he went mad and ended up killing six million Jews."
He was later confronted outside the BBC's studios by Labour MP John Mann, who accused him in front of TV cameras of being a "Nazi apologist".
And he was later suspended by Labour leader Jeremy Corbyn, who said there had been "grave concerns" about the language used.
Mr Corbyn tweeted on Saturday: "There is no place for anti-Semitism or any form of racism in the Labour Party, or anywhere in society."
Shadow chancellor John McDonnell said: "I just wish Ken would have apologised for some of the offence that he's caused. I know he's said he regrets what he's said, but I think he should now apologise."
The row comes less than a week before local elections in England, and for the devolved administrations in Scotland, Wales and Northern Ireland.
Mr Livingstone, who has been a close ally of Mr Corbyn and his left-wing ideals, said he believed the attacks against him were coming from the right-wing of the party and were really aimed at undermining the leadership.
"The really appalling thing here is dishonest MPs who know that what I said is true have stirred up all this nonsense because they want to damage our chances at the local election so they then have a chance of undermining Jeremy."
Shadow cabinet minister Jonathan Ashworth said it was Mr Livingstone who was undermining Mr Corbyn, and urged him to "put a sock in it".
He told the BBC: "I was offended by Ken's remarks. I think Ken crossed a line. I'm not a bitter former Blairite... I am proud to serve in Jeremy's shadow cabinet."
Anti-Semitism and Zionism
- Anti-Semitism is "hostility and prejudice directed against Jewish people" (OED)
- Zionism refers to the movement to create a Jewish state in the Middle East, corresponding to the historic land of Israel - anti-Zionism opposes that
- Some say "Zionist" can be used as a coded attack on Jews, while others say the Israeli government and its supporters are deliberately confusing anti-Zionism with anti-Semitism to avoid criticism.
Israeli PM Benjamin Netanyahu provoked widespread criticism in October when he said a Palestinian leader persuaded the Nazis to carry out the Holocaust.
Mr Netanyahu insisted Adolf Hitler had only wanted to expel Jews from Europe, but that Grand Mufti of Jerusalem Haj Amin al-Husseini had told him: "Burn them."
However, the chief historian at Israel's memorial to the Holocaust said this account was factually incorrect.