Jon Lansman, founder of the influential Momentum organisation, is reported to be among Labour figures urging Mr Corbyn to drop his opposition to the full International Holocaust Remembrance Alliance (IHRA) definition.
It comes days after Tom Watson, Labour’s deputy leader, said he supported the IHRA definition and wanted the party to adopt it.
The latest calls are likely to pile fresh pressure on Mr Corbyn to change tack after the Labour leadership faced sustained criticism over its handling of antisemitism. They also expose the rift among allies of the Labour leader over how the antisemitism crisis should be handled.
The Independent understands Mr Lansman, John McDonnell, the shadow chancellor, and some trade unionists are urging a more conciliatory approach, while some of Mr Corbyn's closest advisers believe he needs to stand firm.
A source close to Mr Lansman told Jewish News: "Like many other leading party members close to the leadership, he recognises the necessity of agreeing that definition in order to be able to begin to rebuild trust with the Jewish community, whatever concerns we may have about the application of some examples.”
The Momentum founder "regretted" that a newspaper article by Mr Corbyn last week "lacked a firm commitment" to the IHRA definition, they added.
Labour has agreed to use the definition in its new code of conduct but has only adopted seven of the IHRA’s eleven examples of antisemitic behaviour. That decision was widely criticised by Jewish groups and the party’s own MPs, reigniting the row over antisemitism.
The Labour leadership is facing mounting pressure to back down and accept the full IHRA definition, and the party’s ruling executive has agreed to consult with Jewish community groups on the matter.
Mr Corbyn is understood to be ready to accept three of the four examples originally omitted by Labour but has maintained his opposition to the fourth, which states that it is antisemitic to deny the Jewish people the right to self-determination, for example by calling the existence of a state of Israel "a racist endeavour".
The other three examples relate to comparing Israeli policies to those of the Nazis, suggesting Jewish people are more loyal to Israel than to their home countries, and holding Israel to different standards to other similar countries.
Mr Lansman had previously defended Labour's new code of conduct, calling it a "gold standard" for other political parties, and voiced concerns about the IHRA definition.
Writing in The Guardian last month, he said: “I regret that for some Jewish communal organisations, the IHRA wording is so sacrosanct that it cannot be expanded and built on, contextualised and turned into a practical document for a party to enforce.
"It cannot be right that one vaguely worded subset of one IHRA example can deny other oppressed groups their right to speak about their own oppression.
“That doesn’t mean that there aren’t contexts in which claims about Israel being a racist endeavour are antisemitic or made with antisemitic intent. But the IHRA’s wording is not sufficiently clear. Labour’s code of conduct provides the necessary explanation.”
Mr Roache, leader of the Corbyn-supporting GMB union, also spoke out about the antisemitism row and insisted the party must adopt the IHRA definition.
Writing for HuffPost, he said: "Antisemitism is a problem in the Labour Party. I’ve been shocked at what I’ve seen on social media. For my entire life, and with every fibre of my being, I have campaigned against and fought racism.
"There is no place for antisemitism in our party, we need to tackle that head-on as well as providing political education and training for members. The Labour movement owes a lot to the contribution of Jewish members and campaigners and the party needs to get to work to rebuild trust across our Jewish communities.
"It is abundantly clear that Labour has to accept IHRA examples of antisemitism in full, while agreeing that criticising the Israeli government and supporting our Palestinian brothers and sisters is not being antisemitic."
It came after the UK's representatives to the IHRA criticised Labour's decision to amend the definition.
They said: "Any ‘modified’ version of the IHRA definition that does not include all of its 11 examples is no longer the IHRA definition. Adding or removing language undermines the months of international diplomacy and academic rigour that enabled this definition to exist."
"If one organisation or institution can amend the wording to suit its own needs, then logically anyone else could do the same. We would once again revert to a world where antisemitism goes unaddressed simply because different entities cannot agree on what it is."
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