Sky News understands disciplinary procedures are under way over the Palestine Live group on the social network, amid allegations anti-Semitic posts were shared.
The group, called Palestine Live, contained posts denying the Holocaust and conspiracy theories about Israeli involvement in 9/11 and the Rothschild family, among other topics.
A Labour spokesman said: 'The Labour Party is committed to challenging and campaigning against anti-Semitism in all its forms.
Mr Corbyn, who was speaking at the Scottish Labour conference in Dundee, criticised the "utter chaos and mismanagement that is defining this Tory Brexit".
Asked what key message he would want to give Corbyn if he had the chance to sit down with him, he said it would not be his role to do so as a former chief rabbi but added: "I would want to see clearer signs of resolute action by a party and its leader before I would even sit down with them full stop".
Mr Murray said he believed the Labour front bench was the biggest impediment to getting single market membership into the Brexit bill but added: "The country is with us, Labour party membership is with us".
An internal Labour probe in 2016 found although there was sometimes a "toxic atmosphere" around anti-Semitism and racism in the party it was not overrun with the problem. But what it does confirm is the long-held suspicion that some anti-Semites use anti-Israel activism as a socially-acceptable outlet for their anti-Jewish prejudice; and that this includes some of this country's leading anti-Israel activists.
A spokesperson for Corbyn, a left-wing politician whom many Jews accuse of tolerating anti-Semitism in the party's ranks, stressed in a comment to The Guardian on Thursday that Corbyn is not alleged to have said anything anti-Semitic in the group, which he left in 2015.
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"We also need to be clear, we could not accept a situation where we were subject to all European Union rules and European Union law, yet had no say in making those laws".
"So, I tell you, if we find any of those in that Facebook group were expressing anti-Semitic views, we will take action against them in the party".
This doesn't mean that most of the members of this group are anti-Semitic, any more than most people who sympathise with the Palestinians are anti-Semitic.
Yesterday, during a visit to Derbyshire, Mr Corbyn said he "removed himself" from the private Palestine Live Facebook group in 2015.
Colin O'Driscoll showed his support on an online page opposing Labour Against Antisemitism (LAAS), which aims to highlight and prevent anti-Semitic abuse within the party.
"We also need to be clear, we could not accept a situation where we were subject to all European Union rules and European Union law yet had no say in making those laws", Mr Corbyn added.
"We strengthened our rules a year ago to guarantee there is no place in Labour for prejudice or bigotry. We are campaigning to increase support and confidence in labour among Jewish people in the United Kingdom".