Jeremy Corbyn has apologised for the hurt caused to Jewish people by anti-Semitism in the Labour party.
In the Observer, Mr Watson said: "This is one of those moments when we have to take a long, hard look at ourselves, stand up for what is right and present the party as fit to lead the nation - or disappear into a vortex of eternal shame and embarrassment".
"I think it is not going to go away until the party adopts the global definition of antisemitism".
But some Labour members fear the growing row over anti-Semitism will damage the party before an election, which is due in 2022.
'People who use anti-Semitic poison need to understand: you do not do it in my name or the name of my party.
Later, Mr Bastani tweeted: "I'm told by multiple sources that Tom Watson did interview attacking the leadership because he didn't get speaking slot he wanted at conference".
David Miliband, a former Labour foreign secretary, was one of the few who stepped forward to offer his support.
When it came to the IHRA rules, Mr Watson said: "We should deal with this swiftly and move on".
Jewish community leaders have insisted the definition should be adopted in full and say it does not prohibit criticism of the actions of the Israeli state.
The Labour MPs, who lost family members in the Holocaust, are facing disciplinary proceedings for confrontations over the party's response to anti-Semitism claims.
"We are acting to speed this process up".
Rosena Allin-Khan, MP for Tooting, said: "It's a sad day when our democratically elected deputy leader is being asked to resign after raising serious concerns about anti-Semitism in our party".
He added: "Aside from what the ongoing anti-Semitism row says about our party, it's unforgivably amateurish that we are allowing our problems to dominate the agenda when the Government should be under the cosh for Brexit, NHS, Universal Credit etc".
"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.
The Labour leader has not conceded on calls to adopt all the examples of contemporary anti-Semitism from the IHRA in its code of conduct.
He said this had "sometimes been used by those wanting to restrict criticism of Israel that is not anti-Semitic".
Gideon Falter, chairman of the Campaign Against Antisemitism NGO, responded to Corbyn's video by saying it was "devoid of any apology for his own antisemitism or promises of specific actions", and added adamantly that "Jeremy Corbyn is an antisemite and under his leadership the Labour Party has become institutionally antisemitic and an existential threat to British Jewry".
Just as in The Guardian, Corbyn failed in the video to address whether the party will accept in full the IHRA definition of anti-Semitism.
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