Jewish lawmaker Margaret Hodge and Ian Austin, whose adoptive parents lost relatives in the Holocaust, are both being probed by party authorities after criticising Labour's failures to stamp out anti-Semitism.
The stance has been backed by Mr Corbyn, who has also vowed to root out anti-semites from Labour ranks. "You are not our supporters", he said.
The Jewish News has reported that Mr Corbyn is now planning to incorporate another three examples, including the idea that it is anti-Semitic to compare contemporary Israeli policies to those of the Nazis, and holding Israel to different standards to other democratic countries. Labour's code adopted the full IHRA definition but misses out four of the 11 examples.
"Why in 2018 do we still find ourselves having to explain the offence this causes to not only Holocaust survivors, but to the Jewish community?"
"We need to listen and respond to their fears".
The Labour leader made the comments in a video released on social media as he and his party continue to be engulfed by scandal over antisemitism.
He said it was important to "de-escalate this disagreement", and believed that it should start with dropping cases against MPs Mrs Hodge and Mr Austin.
Making matters more fraught, the party has launched disciplinary action against two of its members of Parliament who harshly criticized Corbyn in the wake of the decision.
"I have frequently had very hard conversations with both Margaret and Ian but what I understand is that your critics are not your enemies".
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"On an issue that is so dear to them, I think people are very, very concerned that these investigations should be dropped quickly".
"We should deal with this swiftly and move on". We can't have this dragging on throughout the summer.
"I think it is not going to go away until the party adopts the worldwide definition of antisemitism". He wished his thanks to Mr Watson for "recognising the gravity of Labour's situation".
"Until Corbyn can honestly and fully own up to the problematic nature of some of his own past actions, he will struggle to lead the cultural change that is needed to clear the decks of a loud minority within Labour who behave in this way", they said.
That provoked a furious and occasionally abusive online campaign aimed at Mr Watson but the senior MP received support from a number of parliamentary colleagues. But he said there was an issue about "half of one example" because it could restrict criticism of Israel.
"Driving antisemitism out of the party for good and working with the Jewish community to rebuild trust are vital priorities", he said.
"He has again preached to Jews that he is right to have rewritten the worldwide definition of anti-Semitism".
Last night Labour Friends of Israel said Mr Corbyn's words would continue to lack credibility so long as he refused to apologise "for the many occasions on which he himself has offended the Jewish community".