Instead of apologising when pressed over his handling of accusations, Mr Corbyn said he was determined that “society will be safe for people of all faiths”.
“I don’t want anyone to be feeling insecure in our society and our government will protect every community,” he added.
In the interview, due to air in full at 7pm, Mr Neil rejected Mr Corbyn’s statements and asked him four times if he would apologise.
Mr Neil added: “So, no apology. I’ve asked you if you wanted to apologise and you haven’t.”
While, the broadcaster tried to move on to talk about Brexit, Mr Corbyn said: “Can I just make it clear, racism in our society is a total poison. Be it Islamophobia, anti-Semitism or any other form of racism.
“I want to work with every community to eliminate it. That’s what my whole life has been about,” he said.
Mr Corbyn’s party has been plagued by allegations of anti-Semitism over the last three years sparking an investigation by the Equality and Human Rights Commission and leading to the suspension of high-profile figures such as Ken Livingstone and Chris Williamson.
Writing in The Times on Tuesday, Chief Rabbi Ephraim Mirvis claimed “a new poison” had “taken root” in the Labour party.
He wrote: “The way in which the [Labour] leadership has dealt with anti-Jewish racism is incompatible with the British values of which we are so proud — of dignity and respect for all people.”
He added: “When December 12 arrives, I ask every person to vote with their conscience. Be in no doubt, the very soul of our nation is at stake.”