Jeremy Corbyn has insisted there is no place in Labour for antisemitism after unprecedented claims from Britain’s chief rabbi that he has allowed the party to become riddled with prejudice.

Ephraim Mirvis accused Corbyn of allowing a “poison sanctioned from the top” to take root in Labour, saying Jews were justifiably anxious about the prospect of the party forming the next government. His remarks prompted support from fellow religious leaders and former MPs.

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

At the launch of Labour’s race and faith manifesto in Tottenham, north London, Corbyn attempted to fight back, saying his party was tackling the problem.

“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,” he said.

“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.”

Mirvis is the UK’s most senior Jewish leader who represents Orthodox Judaism. In a highly unusual intervention in politics, he argued that the soul of the nation was at stake.

Writing for the Times (£), he said it was not his place to tell people how to vote but argued that the way in which the Labour leadership had dealt with antisemitism was “incompatible with the British values of which we are so proud – of dignity and respect for all people”.

Labour has strongly denied any suggestion that Corbyn has failed to get to grips with allegations of antisemitism, pointing to his record as an anti-racist campaigner and moves to overhaul the party’s complaints process.

On Tuesday he avoided addressing Mirvis’ claims head-on, instead saying: “Sometimes, when people are challenged they say: ‘Are you tolerant of somebody else? Are you tolerant of somebody who has a different face to you or a different appearance to you?’

“I don’t like that word tolerant. I don’t tolerate people. I respect people. So, let’s do it on the basis of respect and inclusion in our society. But let’s also be clear: abuse and racism in any form is not acceptable in any way in 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 leader said if he got into government he would like to speak to all faith leaders and invited Mirvis to meet him.

“I want to lead a government that has an open door to all of the faith leaders, so I invite the chief rabbi, I invite the archbishop of Canterbury, I invite all the other faith leaders to come talk to us about what their concerns are.

“But be absolutely clear of this assurance from me. No community will be at risk because of their identity, faith, their ethnicity, their language,” he said.

At the launch, 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, in so far 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.

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. Some have accused Corbyn of endorsing antisemitic tropes and imagery.

Following Mirvis’s comments, Berger, who is standing as a candidate for the Liberal Democrats, said: “Unprecedented and devastating intervention from the chief rabbi. 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.”

The chief rabbi’s comments overshadowed the announcement of new anti-racist policies including a new public body to oversee the legacy of colonialism, a race equality unit at the Treasury and reduced charges for Home Office documents and tests.

The policies, launched by Corbyn, Dawn Butler, the shadow equalities secretary, and Diane Abbott, the shadow home secretary, follow a party-wide consultation since September.

Among the policies is the creation of what would be called an emancipation educational trust. Based around examining historical injustice, it would ensure that the role of the British empire is taught in schools.

The plan, some elements of which appear in the main Labour manifesto, would also cover a review into the lack of BAME teachers in schools, and an outside review into the issue of far-right extremism.

Appearing on a stage at the Bernie Grant arts centre, Tan Dhesi, who is hoping to be re-elected as MP for Slough, said the new race manifesto would also call for an independent inquiry into the storming of the golden temple and an official apology for the 1919 Amritsar massacre.

Abbott reminded Labour activists that they, like the late MP Grant, who entered parliament at the same time as her in 1987, should not back down on their beliefs if they were criticised by others.

“It is important to remember that just because you are vilified in the here and now does not mean that you are not right,” she said.

Afzal Khan, the shadow immigration minister, said Labour should not shy away from trying to tackle international issues while combatting antisemitism. “We need to heal this issue about Israel and Palestine as well. We need to do it in a fair and just manner,” he said.

Responding to the chief rabbi’s comments during a campaign trip in Scotland, Boris Johnson said Corbyn was guilty of a failure of leadership.

The prime minister added: “I do think it’s a very serious business when the chief rabbi speaks as he does. I have never known anything like it, and clearly it’s a failure of leadership on the part of the Labour leader that he has not been able to stamp out this virus in the Labour party.

“But I’m afraid it’s accompanied with a general failure of leadership we’re seeing at the moment on Brexit.”