Jess Phillips has accused her rivals in the race to succeed Jeremy Corbyn of “keeping quiet” about antisemitism, as the party’s failure to root out racism in its own ranks triggered heated exchanges at the first leadership hustings.

For the first 40 minutes, the five surviving contenders engaged in civilised debate and avoided any personal criticism of one another, broadly agreeing on the shortcomings of the last election manifesto and the need to end factionalism. But, after the panel was asked about antisemitism, Phillips’s remarks changed the mood .

Referring to her own repeated calls during Corbyn’s time as leader for an independent complaints procedure to investigate cases involving Labour party members, the MP for Birmingham Yardley told the meeting in Liverpool: “The Labour party needs a leader who has spoken out against antisemitism and other forms of harassment.

“When others were keeping quiet – as someone who was in the room struggling for an independent system during lots and lots of meetings … I don’t remember some of the people here being in that particular room or in those particular fights when we were really pushing for this to change.

“Jewish people were scared of the Labour party winning the election. That is deeply serious ... we have lost the moral high ground to fight racism in this country because of the way we have handled antisemitism.”

Phillips did not specify which of her four rivals – Rebecca Long-Bailey, Emily Thornberry, Lisa Nandy and Keir Starmer – she had in mind. But officials involved with her campaign said she was determined to point out that not everyone battling for the leadership had backed the kind of tough action she had advocated and at least one had actually argued against an independent complaints procedure in the shadow cabinet.

The comments goaded Phillips’s rivals to launch spirited defences of their own roles in the long-running antisemitism crisis. Thornberry said: “I tell you what, Jess, I have always been clear about it and I always will be because it’s unacceptable, it undermines us as a party and undermines our soul. What we should be doing is kicking out these antisemites.”

Starmer also defended his record and insisted he had called regularly for more action from Corbyn and his team. “If you are antisemitic you should not be in the Labour party. I have spoken out on radio on the media, I have spoken out about the rule changes I thought we should adopt, and I have also spoken in shadow cabinet and plenty of others have done so, so don’t think there hasn’t been an argument.”

Nandy, the MP for Wigan, said the way the leadership had handled the issue still haunted her. “I never ever want to see again the sight I saw at the Parliamentary Labour party of a group of Jewish Labour MPs begging the party to adopt an internationally recognised definition of antisemitism and the response that came from the top table was that ‘we know better than you what constitutes antisemitism’. The failure of leadership at the top of this party has let us all down.”

Long-Bailey, who had responded to the question on how Labour should eradicate antisemitism before Phillips, said she was appalled that some people had not voted Labour because they thought it was antisemitic. She said the partly needed to improve and speed up its complaints procedures and remember it was “the party of the Lever brothers and Ralph Miliband”.

This week will be crucial for the five contenders as they try to win enough support from the unions and constituency Labour parties to get on the ballot paper. The shopworkers’ union Usdaw will make its choice before the GMB – which is expected to back Nandy – decides on Tuesday. Then on Friday the country’s second-biggest union, Unite, is expected to come in for Long-Bailey, who last week also won the support of the pro-Corbyn movement Momentum. Starmer has already received endorsement of the country’s largest union, Unison. Candidates must be supported by either 5% of all constituency Labour parties or three Labour affiliates – of which at least two must be trade unions – in order to proceed. The Jewish Labour Movement, an affiliate, is yet to decide which contender to back.

On a visit to Grimsby on Monday Nandy will say that under her leadership, Labour would support UK firms being given contracts in sectors such as the offshore wind industry, rather than overseas companies taking on the work. She has also pledged to use British Steel in all government contracts as part of a pitch to secure more jobs for UK workers.