The extraordinary open letter from the Board of Deputies of British Jews and the Jewish Leadership Council came as Mr Corbyn said he was “sincerely sorry” for the pain caused by “pockets” of anti-Semitism within Labour.
But the Jewish leaders took aim at Mr Corbyn personally, saying he is “repeatedly found alongside people with blatantly anti-Semitic views” but “claims never to hear or read them”.
The organisations plan to protest outside Parliament before delivering an open letter to a meeting of Labour MPs and peers at which concerns about anti-Semitism are expected to be raised - although Mr Corbyn will not attend.
In their letter they said: “Today, leaders of British Jewry tell Jeremy Corbyn that enough is enough.”
They said there was a “repeated institutional failure” to properly address Jewish concerns and to tackle anti-Semitism.
“We conclude that he cannot seriously contemplate anti-Semitism, because he is so ideologically fixed within a far-left worldview that is instinctively hostile to mainstream Jewish communities.”
The latest row was triggered by a Facebook comment from 2012 when Mr Corbyn offered a show of support for the painter of a mural at the centre of an anti-Semitism row whose controversial street art was about to be painted over.
Mr Corbyn later said he sincerely regretted not looking properly at the “deeply disturbing and anti-Semitic” picture before telling Mear One he was in “good company” among artists who had work removed.
The British Jewish leaders’ statement said: “When Jews complain about an obviously anti-Semitic mural in Tower Hamlets, Corbyn of course supports the artist.
“Hezbollah commits terrorist atrocities against Jews, but Corbyn calls them his friends and attends pro-Hezbollah rallies in London. Exactly the same goes for Hamas.”
They added: “Again and again, Jeremy Corbyn has sided with anti-Semites rather than Jews.
“At best, this derives from the far left’s obsessive hatred of Zionism, Zionists and Israel.
“At worst, it suggests a conspiratorial worldview in which mainstream Jewish communities are believed to be a hostile entity, a class enemy. “
The statement said Jews faced “fundamental anti-Semitic slurs” in Labour meetings or online forums on a daily basis and “rightly or wrongly, those who push this offensive material regard Jeremy Corbyn as their figurehead”.
He was “the only person with the standing to demand that all of this stops”.
The Labour leader did not make any reference to the criticism aimed at him personally in his statement.
But in a message aimed at building bridges with the Jewish community he acknowledged that Labour must demonstrate a “total commitment to excising pockets of anti-Semitism that exist in and around our party”.
The Labour leader said he would meet representatives from the Jewish community over the coming days.
Mr Corbyn said: “Labour is an anti-racist party and I utterly condemn anti-Semitism, which is why as leader of the Labour Party I want to be clear that I will not tolerate any form of anti-Semitism that exists in and around our movement. We must stamp this out from our party and movement.
“We recognise that anti-Semitism has occurred in pockets within the Labour Party, causing pain and hurt to our Jewish community in the Labour Party and the rest of the country.
“I am sincerely sorry for the pain which has been caused.”
Labour MPs Ian Austin and Wes Streeting said they were “ashamed” of the way the party’s relationship with the Jewish community had deteriorated.
Former Cabinet minister Yvette Cooper said Mr Corbyn should apologise for his own actions.
She told Channel 4 News: “I think that it would be right for Jeremy to give a full apology for the comments that he made.”