Prominent Labour figures have called on Jeremy Corbyn to do more to “root out” anti-Semitism from within the party.
Ex-prime minister Tony Blair said the time for words was over and told Mr Corbyn to show he is “prepared to act”.
Luciana Berger, chair of Jewish Labour, said anti-Semitism was a “stain on the conscience of the party” while one MP warned Labour had become a “cesspit” for anti-Semitic views.
Mr Corbyn has said he wants to meet Jewish groups to hear their concerns.
Protesters gathered outside Parliament on Monday, joined by Labour MP Ms Berger, demanding action from the Labour leader.
Jewish leaders have accused Mr Corbyn of not doing enough to tackle anti-Semitic abuse, and in a strongly-worded open letter told him “enough is enough”.
In his response, Mr Corbyn acknowledged anti-Jewish prejudice had surfaced within Labour and it had been wrong for some people to dismiss it “as a matter of a few bad apples”.
He pledged to “redouble” his efforts to ensure there was zero tolerance of anti-Semitism, by dealing with cases more quickly and improving political education among activists.
Mr Blair said Mr Corbyn would be “very wise” to listen to the concerns being expressed about anti-Semitism within the party – and told the Labour leader to “root it out, completely, 100 per cent”.
“I don’t believe he is personally anti-Semitic, no I don’t actually,” he told Newsnight.
“But I do believe he and the people around him, particularly, do not understand the seriousness of this problem.
“Up to now at least, they have not really got it… What I would urge the Labour leadership to do, collectively, is to recognise this is a real problem.
“It’s got beyond the stage where words will solve this… He is going to have to show that he really understands the issue, that the people around him really understand it, and that he’s prepared to act on it.”
Mr Blair, who became a Middle East envoy after leaving power in 2007, has long been accused by the left of having too cosy a relationship with successive Israel governments.
Asked if he was conflating legitimate criticism of Israeli policy with anti-Semitism, Mr Blair said activists could oppose the actions of individual governments but “that’s different from being anti the state of Israel and its existence – and when people are in that position it very quickly trends across into anti-Semitism”.
In his letter to the Jewish Leadership Council and the Board of Deputies of British Jews, Mr Corbyn acknowledged “newer forms of anti-Semitism had been woven into criticism of Israeli governments”.
While criticism of Israel could not be avoided, he said it was simply wrong to hold all Jewish people responsible or to attribute criticism of Israeli governments to Jewish characteristics, adding he would be a militant ally against all forms of anti-Semitism.
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A succession of Labour MPs made their feelings known at Monday’s demonstration in Parliament Square and at a subsequent meeting of the Parliamentary Labour Party.
Louise Ellman, a former vice-chair of Labour Friends of Israel, said Mr Corbyn’s supporters should not be allowed to dismiss anti-Semitism as smears against their leader.
“No more turning of a blind eye, no more failing to recognise anti-Semitism on the left as well as the right,” she told the BBC’s Newsnight.
Shadow Transport Secretary Andy McDonald said Mr Corbyn had apologised for recent cases of anti-Semitism but also for appearing to question the removal of a 2012 anti-Semitic mural rather than condemn it.
“We treat this matter extraordinarily seriously,” he said.
“We know exactly what this means and I want people to have no illusions whatsoever that the Labour Party will deal with this and deal with this properly.”
He said disciplinary cases, including that of former London Mayor Ken Livingstone, were taking far too long.
Jonathan Arkush, president of the Board of Deputies of British Jews, said the Labour leader simply needed to confront and expel anti-Semites from the party.
“He’s clearly trying to make up some ground but in the end it’s about actions and not words,” he said.
“We’ve had lots of words from Jeremy Corbyn before. He always declares himself to be an enemy of racism. The trouble is he still hasn’t confronted or taken effective action.”
Jenny Manson, from Jewish Voices for Labour, said there was anti-Semitism in parts of the party as well as society at large but she questioned whether it was “institutionally rampant” as some have suggested.
She also suggested there was less press coverage of anti-Semitism on the far right.