Labour's anti-Semitism row needs to be resolved "as soon as possible", shadow chancellor John McDonnell has said, adding: "It's shaken us to the core."
Issues like the party's code of conduct urgently need to be settled, he added.
He was speaking after Jeremy Corbyn apologised over a 2010 event he hosted, where a Holocaust survivor compared Israeli policy to the Nazi regime.
Mr Corbyn said he "completely rejects" the views of some people he had shared platforms with in the past.
It comes as an ally of the leader faces calls to quit the party's ruling body after criticising "Trump fanatics" in the Jewish community, and with the party facing criticism from Jewish leaders and some of its MPs over its new anti-Semitism code of conduct.
Mr McDonnell said: "None of us fail to appreciate, I suppose, the way this has upset people including ourselves. It really has shaken us to the core really, but we'll resolve it, we've got to."
Mr McDonnell said Jewish people were "really suffering out there", citing a "massive increase in attacks", graffiti daubed on cemeteries and security guards for Jewish schools.
"So we've got to resolve the issue within our party and then get out there to assist the Jewish community campaigning against anti-Semitism within our society overall," he added.
The House of Commons event hosted by Mr Corbyn took place on Holocaust Memorial Day in 2010. Jewish Auschwitz survivor and anti-Zionist Hajo Meyer, who died in 2014 aged 90, compared Israeli policy to the Nazi regime.
The Commons meeting came during a wider tour by Mr Meyer entitled "Never again for anyone - Auschwitz to Gaza".
The Times said that Palestinian activist Haidar Eid also addressed the meeting, saying, "the world was absolutely wrong to think that Nazism was defeated in 1945. Nazism has won because it has finally managed to Nazify the consciousness of its own victims".
Mr Corbyn said views were expressed which he did not "accept or condone".
He added: "In the past, in pursuit of justice for the Palestinian people and peace in Israel/Palestine, I have on occasion appeared on platforms with people whose views I completely reject.
"I apologise for the concerns and anxiety that this has caused."
Analysis: Labour stuck in cul-de-sac of blame
By BBC political correspondent Ben Wright
Prominent Jewish voices inside and outside Labour are furious that the leadership seems to claim a clearer idea about what constitutes anti-Semitism than they do.
Neither the actions nor words of Jeremy Corbyn have managed to calm this argument down.
And while the government struggles to keep its plan for Brexit on the road, Labour appears to be stuck in a cul-de-sac of blame and recrimination on how it's tackling anti-Semitism.
A Labour MP has also called for an investigation into Mr Corbyn after a video of him praising the release of convicted terrorists from Hamas emerged.
The Times shared the video of the Labour leader who appeared on Iranian state TV in 2012.
He referred to the terrorists as "brothers" and questioned whether there was a "serious case" against them.
Joan Ryan, who represents Enfield North, has told the paper the interview was "abhorrent" and "brings the Labour party into disrepute".
Labour has faced criticism over its new code of conduct on anti-Semitism, which critics claim does not sign up fully to the International Holocaust Remembrance Alliance's working definition.
Labour says it has included the full International Holocaust Remembrance Alliance definition but has rewritten four of the examples included to expand and contextualise them "to produce legally robust guidelines that a political party can apply to disciplinary cases".
One of the examples changed was the IHRA's one saying: "Drawing comparisons of contemporary Israeli policy to that of the Nazis."
Labour's code of conduct instead says: "Discourse about international politics often employs metaphors drawn from examples of historic misconduct. It is not anti-Semitism to criticise the conduct or policies of the Israeli state by reference to such examples unless there is evidence of anti-Semitic intent.
"Shami Chakrabarti recommended that Labour members should resist the use of Hitler, Nazi and Holocaust metaphors, distortions and comparisons in debates about Israel-Palestine in particular. In this sensitive area, such language carries a strong risk of being regarded as prejudicial or grossly detrimental to the party."
Following the row, the party's MPs will vote in September on whether to adopt the full IHRA wording after passing an emergency motion last week.
'Break the impasse'
Labour MP John Mann, a long-standing critic of Mr Corbyn, told BBC Radio 4 Today that hosting an event called "Auschwitz to Gaza" on Holocaust Memorial Day breached anti-Semitism rules and "breaches any form of normal decency".
"I've no idea how he got himself into that situation, but I'm glad that he has apologised and on the back of that apology is the opportunity to do something significant," he said.
Ann Black, a member of Labour's National Executive Committee and a supporter of Mr Corbyn, urged him to follow the advice of shadow cabinet colleagues and adopt the working definition on anti-Semitism.
She told Today that, if necessary, the party could add assurances that members were free to defend Palestinians or criticise the Israeli government.
"I don't think Jeremy Corbyn is in any way racist or anti-Semitic. I do believe he has the authority and the ability to break the current impasse," she said.