The meeting with the Jewish Leadership Council (JLC) and Board of Deputies for British Jews in Mr Corbyn's office lasted 90 minutes longer than scheduled, but ended without agreement. "Our sole objective from this meeting was to build trust with Mr Corbyn, but this will not be possible until and unless he and the party turn their many strong words against anti-Semitism into equally strong actions in order to bring about a deep cultural change in his supporters" attitude to Jews'.
He also said that over 20 officials had been expelled from the party in the past two weeks due to anti-Semitic behavior, with many more now under investigation.
It said he did not agree to proposals for a "fixed timetable" to deal with allegations of anti-Semitism in the party and to expedite long-standing cases - including that of former London mayor Ken Livingstone, who was previously suspended from Labour over anti-Semitism accusations.
"It was against Corbyn's handling of anti-Semitism".
"When members of Jewish communities express genuine anxieties, we must recognize them as we would those of any other community", the opposition leader wrote on Facebook.
Asked if Mr Corbyn had shown leadership on the issue, Mr Gwynne sidestepped the question, saying: "I think what we have now got to do - and we have got an issue in the Labour Party - we have got to acknowledge that that problem exists and, for some, that is a challenge". We will continue to engage and work with Jewish community organisations to deal with this issue.
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Corbyn, however, described the meeting as "positive and constructive", and vowed to take further steps to combat the phenomenon. "Our party will not fail our Jewish brothers and sisters", the Labour leader said. He has himself faced questions about his own links to known anti-Semites, past comments on Israel, and associations with vehemently anti-Israel figures.
"The Labour Party needs to make sure anti-Semitism doesn't exist within the party, one anti-Semitic Labour member is one too many. And that of course goes for the Labour Party too".
"Whilst there was a number of issues raised, actually many of those issues we agreed to either implement or we were already implementing or we agreed to do something in more detail".
"My party and I are sorry for the hurt and distress caused".
But in their statement, they said: "We are disappointed that Mr Corbyn's proposals fell short of the minimum level of action which our letter suggested".
Expectations before Tuesday's meeting were low, reported British broadcaster ITV, with little progress being made in preparatory discussions on Monday between representatives from the Jewish groups and Seumas Milne, Corbyn's director of strategy and communications.