Sky News understands disciplinary procedures are under way over the Palestine Live group on the social network, amid allegations anti-Semitic posts were shared.
Mr Murray and his ally, the former Scottish Labour leader Kezia Dugdale, have challenged the leadership of Mr Corbyn and Scottish chief Richard Leonard by launching a campaign group opposing their refusal to stay in the single market.
Corbyn said his posts were limited to some replies, including "a suggestion on the vote on recognising Palestine, which I supported, and inviting a doctor to speak at an event".
"Had I seen it, of course, I would have challenged it straight away but I actually don't spend all my time reading social media", he said.
And because the most active members of this Facebook group also tend to be the more anti-Semitic ones, their views set the tone for the group as a whole.
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"I removed myself from the group in 2015". "Obviously, any antisemitic comment is wrong".
"Any anti-Semitism in any form is wrong".
It also supports the findings of Britain's largest-ever survey of anti-Jewish and anti-Israel attitudes, published a year ago by CST and the Institute for Jewish Policy Research, which found that the more anti-Israel a person is, the more likely they are to also hold anti-Jewish attitudes. I was not aware that I was added to this group nor have I participated in it. Clive Lewis MP appeared to be a member, as did Corbyn's son, Seb, and a key member of his inner team, Jack Bond.
At a Derbyshire County Council (DCC) meeting last month, Councillor Alex Dale, cabinet member for young people at the Tory-led authority, referred to Labour politicians who had been accused of making anti-Semitic remarks.
Indeed, of the three "admins" who run the group, one - the group's founder - is a conspiracy theorist who shares material from Holocaust Denial websites; a second identified himself as a "9/11 Truther" and posted a Holocaust Denial article that dismissed the "fictional account" of six million Jews dying in the Holocaust, claiming instead that "somewhere between 100-150 thousand people perished in Auschwitz mainly as a result of disease and starvation"; while a third admin posted an article in the group titled "Israel Control of USA Government" that quoted approvingly from Mein Kampf. "I am very very careful, it is a secret group".
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In an address to the party's Scottish conference in Dundee, he said a future Labour government could be "held back" under a deal which forced it to follow the same rules as other European Union states.
"I don't think anyone is suggesting that anything that Jeremy has written in any Facebook group or anywhere else constitutes antisemitic comments", he said.
The screenshots include discussions in which group members use terms such as "JewNazi" and "ZioNazi".
"It is repugnant if there are antisemitic posts - and I gather there are".
The spokesman said: "Jeremy and the Labour Party are implacably opposed to all forms of anti-Semitism and will take whatever necessary action to stamp it out in the Labour Party".
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Palestine Live's content was first revealed in a 250-page dossier looking at the posts and profiles of members of the group, compiled by the businessman David Collier, who said his blog was dedicated to "researching antisemitism inside anti-Zionist activity".