Lisa Nandy, who was widely hailed as the best performer on the night, said: "I believe Jewish people have a right to national self-determination. That makes me a Zionist.”
Even Rebecca Long Bailey, the candidate accused of representing "continuity Corbyn", said: “I also agree with a secure Israel and I also agree with a two-state solution, I suppose that makes me a Zionist because I agree with Israel's right to exist and self-determine."
Sir Keir had initially tried to explain his support for both a "secure Israel" and an "independent Palestinian state."
Mr Peston suggested this effectively meant he was, in a similar way to JLM, a "Zionist."
But the Holborn and St Pancras MP added: "I don't know how many people know this - my wife's family are Jewish and we have got extended family in Israel.
"I don't describe myself as a Zionist but I understand and I sympathise and I support Zionism.
"I wouldn't describe myself in that way - but of course we have family in Israel and that is part of my family."
In a 90-minute debate, all four leadership hopefuls expressed regret over the antisemitism crisis that engulfed Labour under Mr Corbyn.
Ms Long Bailey said widening the party's membership had allowed antisemites join the party and conspiracy theories and tropes had circulated online.
She claimed: "I did speak about this in shadow cabinet at times - but did I do enough? Could I have done more? Yes."
She added it would "take time" to heal the rift the Jewish community.
But Mr Peston slammed processes within the party, saying they were "to use a technical term, s**t."
He then read out a statement Mr Corbyn had taken to a 2018 meeting of the party's ruling body, that suggested the very formation of the State of Israel was "racist."
Mr Peston added: "It was the time of the debate around the IHRA definition. Jeremy brought forward a compromise statement that was straight-fowardly antisemitic."
Ms Long Bailey claimed she herself was fully in support of IHRA, which has previously been disputed.
But Ms Thornberry said: "I remember we spent the whole summer wrangling. I went in and said the extreme interpretations of IHRA that some people were banding about were just something we should not be worrying about."
She also said she was told it was "not my business" to express concern Labour was losing the trust of the Jewish community.
Sir Keir added the "process were bad and they were slow" and "there was a lack of leadership."
He claimed he had spoken out repeatedly on BBC Radio Four's Today and Mr Peston's own ITV show about accepting the IHRA definition.
He added: "I went and saw Jeremy."
In defence of Ms Thornberry, he said she had spoken up "loud and clear" on antisemitism in shadow cabinet meetings.
"The NEC aren't doing anything about it," Ms Thorberry claimed to have said.
Ms Nandy - who had resigned from the shadow cabinet in 2016 after publicly criticising the failure to act over antisemitic social media messages by MP Naz Shah - said: “I’ve considered my position in the Labour Party… I’ve questioned that every single day.”
She earlier received loud applause with her comment that antisemitism was "different from other forms of racism, it punches up not down."
She said Jews were left being attacked as "privileged" and racist themselves.
The Wigan MP spoke of being accused of "disloyalty" for attempting to speak out on antisemitism.
During the hustings - promoted also by the Jewish News and Labour Friends of Israel - the candidates were asked about the whistleblowers who had spoken out on BBC Panorama about the failure to tackle anti-Jewish racism.
Mr Peston also asked whether the party should settle the legal claims some had launched against it.
Some were in the audience on Thursday evening.
Ms Long Bailey said: I don’t think the party gave the right response.
"We should not have called out or attacked former members of staff… We should apologise for how we behaved. We should settle any claims that were made.”
Ms Nandy replied: “I want to do more than just settle… I will make the Labour Party one that values and celebrates that sort of action.”
Sir Keir said: “I remember that programme well and being shocked by the response that was put out … I remember what I said to Jeremy.
"I said I’ve never been in an organisation that turns on its staff before, ever. Because what message do you think that sends not just to the ex-staff but current staff who speak out.
"They will be branded disloyal. I think it was utterly wrong that statement was put out and I said that directly the next morning.”
He said of the equality watchdog's investigation into the party, which due to be published in May: “I’ve said we’ve got to ask for preliminary findings.”
All candidates said they would welcome Dame Louise Ellman and Luciana Berger, two Jewish MPs who quit over antisemitism, back into the party.
In a clash of opinion, Ms Nandy said the crisis over social care in the country could be helped by a “cross-party consensus” and need to “reach across the political divide.”
Ms Thornberry said: "It ain't going to happen."
At the start of the event, JLM national chair Mike Katz and new JLM parliamentary chair Dame Margaret Hodge had criticised Labour's continued failure to throw out all its antisemites.
"It's make or break time for Labour and Jewish community," said Mr Katz.
Dame Margaret read out some of the abusive and antisemitic messages sent to herself and former Labour MP Ruth Smeeth, who also attended the event.
At the end, Mr Peston asked for a show of hands from the audience on who would consider backing Labour again having heard the candidates speak.
Nearly all inside the shul raised their arms.
JLM is expected to announce whom it has nominated in the leadership contest at midday on Friday after polling members.
