The Board of Deputies (BoD) and Jewish Leadership Council (JLC) said there were “disappointing missed opportunities” after a meeting with the Labour leader on Tuesday afternoon.
They accused Mr Corbyn of “failing to agree to any of the concrete actions” they had proposed in a letter to him in March.
The Labour leader responded by calling the two-hour session a “positive and constructive meeting”.
Earlier, he wrote an article for the Evening Standard admitting that “my party and I are sorry for the hurt and distress caused” from Labour’s ongoing row over anti-Semitism.
But Jonathan Arkush, president of the BoD, and Jonathan Goldstein, chair of the JLC, hit back, saying that “words in letters and newspaper articles will never be enough”.
They said in a statement: “We welcome the fact that Mr Corbyn’s words have changed but it is action by which the Jewish community will judge him and the Labour party.
“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.”
They said Mr Corbyn did not agree with proposals there should be a fixed timetable to deal with complaints of anti-Semitism against Labour members.
Nor did the Labour leader allegedly endorse expediting the long-standing cases involving former London mayor Ken Livingstone or former Momentum vice-chair Jackie Walker.
“Every excuse given by Mr Corbyn and his team was wrapped up in process,” they complained. “We feel that the excuses of process are just another excuse of inactivity.”
The Labour leader had a different take on the meeting, writing in a post on Facebook that he was “grateful” and “absolutely committed to rooting out anti-Semitism from our party and our society”.
“When members of Jewish communities express genuine anxieties, we must recognise them as we would those of any other community.
“Their concerns are not ‘smears’. Jews belong in the Labour Party and we are utterly committed to making it a safe and welcoming place for them…
“We will lay out the further steps we are taking in the coming weeks. We will continue to engage and work with Jewish community organisations to deal with this issue. Our party will not fail our Jewish brothers and sisters.”
The meeting follows a protest of hundreds outside Parliament last month, with demonstrators chanting “enough is enough” to demand Mr Corbyn root out all anti-Semites from Labour.
Labour MP Ian Austin wrote on Twitter following the meeting: “How could Labour leadership watch unprecedented protest by Jewish community and last week’s debate and still fail to deal with their concerns?”
But Andrew Gwynne, Labour’s shadow communities secretary, suggested it was wrong to claim Mr Corbyn ignored requests for concrete action.
“That’s not my understanding of what was agreed,” he said. “I’m not sure how they’ve interpreted the meeting.
“Many of those issues we agreed to implement, or we were already implementing – or we agreed to consider them in more detail.”