"And in the West Bank [the people are] under occupation of the very sort that would be recognised by many people in Europe who suffered occupation during the Second World War with the endless roadblocks, imprisonment, and irrational behaviour by the military and the police", the pro-Palestinian campaigner said.
A former Labour cabinet minister has taken out a full-page advertisement in a Jewish newspaper to lambast Jeremy Corbyn's "intellectually arrogant, emotionally inept and politically maladroit" approach to the party's antisemitism crisis.
But the Labour Party insisted Mr Corbyn was not comparing the Israeli State with Nazis.
PA Wire/PA Images Labour leader has come under increasing pressure to tackle the anti semitism engulfing the party.
Murphy said there was "a small, but growing minority, of antisemitic conspiracy theorists amongst the membership of the Labour Party".
Murphy's dramatic intervention increases pressure on Corbyn and Labour's National Executive Committee to reconsider the code of conduct on anti-Semitism agreed last month, which omits four of the International Holocaust Remembrance Alliance examples from its own list of unacceptable behaviours.
Murphy said that under Corbyn, Labour appeared to have "deliberately turned its back on British Jewry".
The Board of Deputies of British Jews accused the Labour leader of refusing to face hard questions about his response to the issue and hoping it would disappear. "Unless he does what he needs to do, it won't", Van der Zyl wrote in an article for Jewish News. I've got some bad news for him.
A Labour spokesman responded to the release of the recording, saying that "Jeremy was describing conditions of occupations in World War Two in Europe, of which there are multiple examples, not comparing the Israeli state to Nazis".
She called for Mr Corbyn to "own up" to the "problematic nature" of his own past actions as well as for transparency in the party's disciplinary process.
Mrs van der Zyl said it was time for him to publicly deal with the issues in the party, warning "you can not lead through invisibility".
"Surely, by now, enough is enough".