Jeremy Corbyn has declined to apologise to the UK Jewish community after the chief rabbi criticised how the party deals with anti-Semitism claims.
In a BBC interview with Andrew Neil, the Labour leader was asked four times whether he would like to apologise.
Mr Corbyn said his government will protect "every community against the abuse they receive".
Chief Rabbi Ephraim Mirvis claimed "a new poison - sanctioned from the very top - has taken root" in Labour.
Following the interview, Labour's Shadow Defence Secretary Nia Griffith said Mr Corbyn should apologise, adding: "We need to apologise to our colleagues in my own party who have been very upset and to the whole of the Jewish community."
Labour has been beset by allegations of anti-Semitism for more than three years, leading to the suspension of a number of high-profile figures such as Ken Livingstone and Chris Williamson, and an unprecedented investigation by the Equality and Human Rights Commission.
In an interview with Andrew Neil on BBC One, Mr Corbyn was asked four times whether he was going to apologise to the British Jewish community following the chief rabbi's claim that Labour was not doing enough to root out anti-Jewish racism.
Mr Corbyn replied: "What I'll say is this I am determined that our society is 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 against the abuse they receive on the streets, on the trains, or in any other form of life."
Mr Corbyn said racism "is a total poison", adding: "I want to work with every community, to make sure it's eliminated. That is what my whole life has been about."
Rabbi Mirvis described Mr Corbyn's claim that Labour had "investigated every single case" of alleged anti-Semitism as a "mendacious fiction".
Challenged about the rabbi's comment, Mr Corbyn said: "No, he's not right. Because he would have to produce the evidence to say that's mendacious."
The Labour leader said he was "looking forward to having a discussion with him because I want to hear why he would say such a thing".
Mr Corbyn also insisted he had "developed a much stronger process" for dealing with allegations and had sanctioned and removed members who were judged to have made anti-Semitic statements.
He added that anti-Semitism allegations "didn't rise after I became leader".
"Anti-Semitism is there in society, there are a very, very small number of people in the Labour Party that have been sanctioned as a result about their anti-Semitic behaviour," he told Andrew Neil.
Speaking in the BBC Wales election TV debate, Ms Griffith, a senior member of Mr Corbyn's team, said the party's handling of anti-Semitism claims was "a shame on us" and "we must absolutely put right".
She added: "We have not been as effective as we should have been in dealing with this problem."
Mr Corbyn was also quizzed about his plan to get a "credible" Brexit deal with the EU and then be neutral in the referendum on the deal he has promised to hold within six months of taking power.
Asked what he would do during the referendum campaign, he said: "I will be the honest broker that will make sure the referendum is fair and make sure that the Leave deal is a credible one.
"That seems to me actually an adult and sensible way to go forward."
Mr Corbyn was also quizzed about Labour's plan to increase income tax on those earning more £85,000 a year to pay for better public services.
He denied many of these people would leave the country under a Labour government, destroying the tax base the party would rely on to fund its plans.
But he said they "could and should" pay more.
"They can see all around them the crumbling of public services and the terrible levels of child poverty that exist across Britain.
"There is no reason why they would have to leave the country and they shouldn't."
Mr Corbyn also said a Labour government would not borrow money "willy-nilly".
"What we are going to do is deal with the worst aspects of what's happened in austerity, the worst aspects of poverty in Britain," he said.
On Labour's policy to compensate some of the women who lost out as a result of changes to the pension age, Mr Corbyn said the women were "short-changed" and a "moral debt" was owed.
The campaign for compensation has been led by the group Women Against State Pension Inequality (Waspi).
Labour says the policy would cost about £58bn, paid in instalments over five years.
When pressed on where this money would come from, Mr Corbyn said it will be paid from government reserves and, if necessary, borrowing, "over some years".
He conceded that there were not sufficient funds in the government's reserves to cover the bill, but insisted the women deserved to be repaid.
"We will make sure they are compensated," he said.
Andrew Neil will be speaking to other party leaders during the election campaign.