The group appears to be at odds with more mainstream Jewish organisations and has suggested anti-Semitism allegations aimed at Mr Corbyn are a smear.
They have also criticised a "narrow Conservative clique" at the head of the Jewish community's major bodies.
The Labour leader offered urgent talks with the two groups after they arranged last week's protest outside Parliament against his handling of anti-Semitism cases.
In response to news of Sir David's departure from Labour at the weekend, a spokesman had said: "As Jeremy said in his email to all members this week, our party is at its best when we work together, uniting people in hope and against fear and division".
"We have to take that seriously, and we have to take every allegation of anti-Semitism seriously even if sometimes people opportunistically seize upon anti-Semitism as an issue to undermine Jeremy, it doesn't matter if that's the reason, we've still got to take the allegation seriously".
Speaking on a campaign visit to Swindon, Mr Corbyn said: "I went to a very interesting and very enjoyable Seder supper and I spent a lot of time talking to young Jewish people about their life in Britain and experiences of anti-Semitism they have had and how they view the future of our country".
Last week, British Jewish groups protested against Corbyn outside parliament, accusing the Labour leader of failing to tackle antisemitism within Labour ranks.
Labour MP John Woodcock, a longtime critic of Corbyn, said it was "irresponsible and dangerous" for him to have met with Jewdas.
Spokesman Ivor Caplin, a former MP, said: "When we called on the leader of our party to show moral leadership and take decisive action to stamp out anti-Semitism, this is not what we had in mind".
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It's all very well planting yourself on the far left of the political spectrum to give your party a clear identity and direction and the nation a shuddering alternative to the status quo at the ballot box, but such re-positioning comes at the price of greater scrutiny of some of the elements within that party - and the results so far have not been good.
The Jewish Labour Movement, who has already criticized Corbyn's relations with the Jewish community, said the Labour leader's presence at the event "topped off the worst week on record of terrible relations between the Labour Party and the Jewish community".
The group added: We are proud to be Jews and proud of everyone who attended, whether they were Jewish or not.
It is hard to imagine how this duplicitous man can claim to be remedying anti-Semitism within the Labour Party.
He added that it was "deliberately baiting the mainstream Jewish community days after they pleaded with him to tackle anti-Semitism".
Corbyn has vowed he would will tolerate "any" anti-Semitism in the party.
Karen Pollock, the chief executive of the Holocaust Educational Trust, claimed that Corbyn's meeting was "clearly deliberate".
Jon Lansman, founder of Momentum, a grassroots organizations responsible for Corbyn's surging support defended the leader and said "I think the important thing is that Jeremy is seeking to meet with mainstream Jewish organizations".
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