Sky News understands disciplinary procedures are under way over the Palestine Live group on the social network, amid allegations anti-Semitic posts were shared.
Some of those reported to have made abusive comments, who are also Labour members, have been suspended from the party.
But, not all of those accused of posting offensive messages about Jews on the group are registered with the party, Sky News has been told.
Mr Corbyn has said he was signed up to the Palestine Live forum without his knowledge and later replied to messages on it, but added he was not fully aware of the group’s content.
“I was joined on to that group without knowing it in probably about 2013/14,” he said.
“I removed myself from the group in 2015.
“I replied by Facebook message to a couple of things about a suggestion on the vote on recognising Palestine, which I supported, and inviting a doctor to speak at an event.
“I have never trawled through the whole group. I have never read all the messages on it. I have removed myself from it.
“Obviously, any anti-Semitic comment is wrong. Any anti-Semitism in any form is wrong.”
The Campaign Against Anti-Semitism has published screenshots of messages purported to have been posted on the group.
Among the reported remarks are allegations about Israeli involvement in the 9/11 terror attacks, as well as links to postings from neo-Nazi groups.
The Campaign Against Anti-Semitism said there was “no conceivable justification” for Mr Corbyn’s involvement in the group and that it would be filing a disciplinary complaint against him to the Labour Party.
Mr Corbyn said Labour “doesn’t tolerate” anti-Semitism “in any form”, adding: “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.”
Speaking to Sky News on Friday, shadow chancellor John McDonnell promised “firm action” if any members of the Facebook group found expressing anti-Semitic views were also linked to the Labour Party.
“If any of those individuals are associated or members of the Labour Party, we will take firm action against them,” he said.
“I know I’ve been criticised at times because I’m quite heavy on this, and I am heavy and so is Jeremy, we will not allow any racists within our party.
“Included in that racism is anti-Semitism. It is appalling and we will not accept it.
“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.”
Mr McDonnell also claimed Mr Corbyn “immediately” left the group when he discovered there were people expressing anti-Semitic views.
But, a senior source within the Labour leader’s office insisted Mr McDonnell’s comments were “not right”.
Instead, Mr Corbyn left the Facebook group, along with others, as part of a “routine” review of his social media accounts when he was elected party leader in 2015 and it was not the case he saw anti-Semitic or offensive messages, the source added.
Mr Corbyn was described as “not an active participant” of the group and merely replied to a small number of messages he was tagged in and received notifications about.
It comes as former chief rabbi Lord Sacks called on the Labour leadership to do more to fight anti-Semitism.
When asked what he would say to Mr Corbyn if he sat down with him, Lord Sacks said: “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.”
Responding to Lord Sacks’ comments, a spokesman for Mr Corbyn said: “Jeremy Corbyn and the whole Labour Party condemns and campaigns against anti-Semitism in all its forms.
“We strengthened our rules last year to guarantee there is no place in Labour for prejudice or bigotry. Our party has deep roots in the Jewish community and is actively engaged with Jewish organisations across the country.
“We are campaigning to increase support and confidence in Labour among Jewish people in the UK.”