Jeremy Corbyn has insisted antisemitism in Labour has not risen under his leadership and resisted calls to apologise to Britain’s Jews, after the country’s chief rabbi claimed he had let poison take root in the party.

In an interview with the BBC’s Andrew Neil, the Labour leader declined four opportunities to apologise for the party’s approach to dealing with antisemitism, which has led a string of Labour MPs to resign and the Equalities and Human Rights Commission (EHRC) to launch an investigation.

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Corbyn, asked whether he would say sorry to Jews on behalf of his party, said: “What I’ll say is this. I am determined that our 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.”

At the end of a bruising day, Corbyn also struggled with questions over how he would fund the party’s £58bn pledge to compensate 1950s-born women hit by a rise in the pensions age – Waspi women – and whether some of his tax rises would hit people on lower incomes.

But he was predominantly pressed on antisemitism, the day after Ephraim Mirvis, the chief rabbi who represents 62 orthodox synagogues, said Jews were justifiably anxious about the prospect of Labour forming the next government.

Corbyn challenged the rabbi’s claims and said he was “looking forward to having a discussion” with him about the accusations.

“It didn’t rise after I became leader,” he said. “Antisemitism 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 antisemitic behaviour.”

In particular, he disputed the rabbi’s statement that Labour was peddling a “mendacious fiction” by claiming it was doing everything possible to tackle anti-Jewish hatred.

The Labour leader told Neil: “He’s not right. Because he would have to produce the evidence to say that’s mendacious.”

Corbyn insisted he had “developed a much stronger process” to deal with accusations of antisemitism, under which officials are sanctioning and removing members who show anti-Jewish prejudice.

However, Neil presented him with the case of a member who has not been suspended and is still being investigated a year after comments came to light saying: “Rothschild Zionists run Israel and World Governments.”

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Corbyn acknowledged this used an antisemitic trope and said the case was still ongoing.

The Labour leader went on to deny the estimates from the Jewish Labour Movement that 130 cases of alleged antisemitism by Labour members are still outstanding, but the party has declined to say how many current complaints are being considered.

While he resisted Neil’s suggestion he should apologise, supporters pointed out that in the summer of 2018, Corbyn said: “I am sorry for the hurt that has been caused to many Jewish people. We have been too slow in processing disciplinary cases of, mostly, online antisemitic abuse by party members. We are acting to speed this process up.”

Neil also pressed Corbyn on how the party would fund compensation for Waspi women. The Labour leader said: “We’ll pay for it because it has to be paid for. It has to be paid for. It’s a moral debt … We will pay for it through either government reserves or if necessary borrow for it.”

On the party’s tax plans, Neil highlighted examples of people earning less than £80,000 who could be hit be tax rises, such as the scrapping of the marriage allowance or a pensioner with modest dividend income.

Corbyn said those losing the marriage tax allowance “won’t get the advantage” and he said the rise in tax on dividends to the level of income tax was “reasonable and fair”.

The Labour leader was also asked whether he would order the shooting of the leader of the Islamic State if there was no way to arrest him. Corbyn said: “Let’s find out what the situation is at that moment in time and what I’ve said all along is we practice international law. We stand by it and abide by international law and if it is possible, only if it’s possible, then you try to capture that person.”

The interview gave little time for Corbyn to talk about his priorities such as funding public services and the NHS, on which he will give a major speech in London on Wednesday.

Earlier in the day, the Labour leader’s launch of a race and faith manifesto was also overtaken by questions about the chief rabbi’s intervention into politics.

Speaking at the event in Tottenham, north London, Corbyn said: “Antisemitism in any form is vile and wrong. It is an evil within our society … there is no place for it and under a Labour government it will not be tolerated in any form whatsoever.

“It was Labour that also passed the Human Rights Act, that set up the Equality and Human Rights Commission. It’s Labour that has to its very core the issues of justice and human rights within our society.”

Responding to allegations that antisemitism has been sanctioned from the top of Labour and that there is anxiety about him becoming prime minister, Corbyn said the party had taken measures to eradicate anti-Jewish hatred, as well as reach out to faith leaders.

He added: “Since I became leader of the party, the party has adopted processes that didn’t exist before … a disciplinary process that didn’t exist before.

“And where people have committed antisemitic acts they are brought to book or if necessary expelled from the party or suspended or asked to be educated better about it.”

The Labour peer Lord Dubs, who came to the UK as a child refugee in 1939, expressed disappointment at the rabbi’s words.

“I am bitterly disappointed by what he said. I don’t accept a lot of what he said, insofar as the Labour party should have acted a lot quicker. But today of all days, for the chief rabbi to be attacking our leader, it is unjustified, unfair and I am bitterly, bitterly disappointed that he has done it,” Dubs said.

Emily Thornberry, the shadow foreign secretary, said “everybody now accepts that we took too long” to deal with antisemitism and that regaining trust was difficult – but she said that Mirvis was wrong to say that it had taken root in the party. John McDonnell, the shadow chancellor, also told ITV he did not think the chief rabbi had “understood the nature of what we’ve been doing and how we’ve been dealing with it”.

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The archbishop of Canterbury, Justin Welby, in effect backed the rabbi’s criticisms with a tweet that highlighted the “deep sense of insecurity and fear felt by many British Jews”.

Labour has faced allegations of antisemitism 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 EHRC investigation.

Some prominent Jewish Labour politicians, including Luciana Berger and Louise Ellman, left the party after being the subject of abuse on social media.

Berger, who is standing as a candidate for the Liberal Democrats, said it was an “unprecedented and devastating intervention from the chief rabbi”.

She said: “During the the last meeting I had with Jeremy Corbyn at the end of 2017, I told him about the many public and private Facebook groups that were littered with antisemitic posts which used the Labour leader’s name and photo in their group name. Nothing was done about it.”

• This article was amended on 27 November 2019 to correct a direct quotation.