Labour would "negotiate a new and strong relationship with the single market", he said, appearing to rule out the call from some in Scotland for the party to commit to permanent membership.
Mr Corbyn's son, Seb, chief of staff to Shadow Chancellor John McDonnell, and Jack Bond, a member of his team, are also thought to be members.
Mr Corbyn confirmed he was signed up to the group without his knowledge but later exchanged messages on it.
One of the contributors to the group announced that he was reading "Mein Kampf" and proposed that "everybody should be forced to read it, especially Jews who have their own agenda as to why they were not liked".
Corbyn said he had not seen the other antisemitic posts on the group. There are also said to be links to articles from far-Right websites.
Corbyn added that he had not seen the anti-Semitic posts on the group.
Euan Philipps, spokesperson for Labour Against Anti-Semitism said the Labour leader had "serious questions to answer" and called for an independent investigation. Last night, it complained about the page after it was discovered by blogger David Collier.
Senior Scottish Labour figures have criticised Jeremy Corbyn's "incredibly disappointing" comments on immigration, likening them to the views of former Ukip leader Nigel Farage.
"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.
Palestine Live is a secret Facebook group that has been running since 2013 and has around 3,000 members who use it to share news stories, organise events and network with like-minded people.
"As anyone knows, in social media all sorts of things are posted which often others participating aren't even aware of", the spokesperson, who was not named, was quoted as saying.
The CAA accuses Mr Corbyn of posting comments in threads that include the term "Zio" - which refers to Zionism.
Ms Dugdale said the Labour party had "allowed the myths of European Union immigration rules to be perpetuated by our own failures to take on these hard arguments for decades". "One of Mr Corbyn's slogans is "standing up, not standing by", but in this case he has not stood up but instead he actively joined in", Glasman said. Home Secretary Amber Rudd announced the cash, which follows £38.5million since 2015.
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.
Addressing the controversy surrounding relations with the Opposition for the first time in an interview marking his 70th birthday today, the peer said: "Any political party has to adopt a zero tolerance approach to anti-Semitism".