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Jeremy Corbyn is set for a crunch meeting with Jewish leaders to discuss what steps he has taken to address anti-Semitism in the Labour Party.
The Jewish Leadership Council and Board of Deputies of British Jews say the Labour leader has been slow to act on the recommendations of a 2016 report.
They want disciplinary cases speeded up and elected officials thrown out if they share a platform with offenders.
Labour says there must be absolute "zero tolerance" of anti-Semitism.
Last month, Mr Corbyn said he was sorry for the pain caused by "pockets of anti-Semitism" in the party and he wanted to "rebuild" confidence among Jewish groups.
He has condemned anti-Semitism on many occasions but his critics, including many of his own MPs, have called on him to back up his words with actions, including expelling former London mayor Ken Livingstone.
He has been suspended since 2016 for claiming Adolf Hitler supported a Jewish homeland in the 1930.
A succession of Labour MPs demanded action from Mr Corbyn in a Commons debate last week, speaking about the abuse they had suffered and warning anti-Semitism had become much more marked in recent years.
A 2016 report by Shami Chakrabarti called for action to address what it said was the "occasionally toxic atmosphere" in the party but it has yet to be implemented in full.
Mr Corbyn has himself been criticised for sending an apparently supportive message to the creator of an allegedly anti-Semitic mural in 2012.
In a message sent via Facebook, he had appeared to question a decision to remove the artist's controversial mural. He later called the mural "deeply disturbing" and backed its removal.
Jewish groups are boycotting a separate round table organised by Mr Corbyn on Wednesday amid concerns about the inclusion of the pro-Corbyn group Jewish Voice for Labour.
The organisation has accused opponents of using the anti-Semitism claims to damage the Labour leader.