Labour MPs and activists are trying to change party rules to make it easier to expel anti-Semitic members, with clear cases to result in a lifetime ban.
Local parties are set to vote on a proposed change in the coming weeks.
The move follows accusations that leader Jeremy Corbyn has been slow to act on prejudice against Jews.
Mr Corbyn has said Labour is "resolute" in tackling anti-Semitism, saying anyone who commits anti-Semitic acts is "auto-suspended" pending an inquiry.
The shadow chancellor, John McDonnell, has said people who express anti-Semitic views should be expelled for life.
But Jeremy Newmark from the Jewish Labour Movement said the party's current rules do not match commitments from Labour's leadership.
Mr Newmark, who also chairs a Labour party branch, told BBC Radio 4's Today programme: "Everybody's talking about zero tolerance of anti-Semitism but it's become apparent because of a spate of incidents over the last couple of months that the rules and processes of the party don't provide adequate provision to deal with it."
He hopes the motion will be accepted by local parties and then adopted by Labour's annual conference in the autumn.
Along with MPs Wes Streeting and Anna Turley he wants a new rule that would ban the use of anti-Semitic, Islamophobic or racist language by members.
It is understood at least one shadow minister will back the initiative.
Mr Streeting said: "We've now got a problem where too many of our Jewish members and people out there in the country think the Labour Party is apathetic to anti-Semitism and it isn't a place for Jewish members.
"I think we've got to make sure that this party with its historic commitment to tackling all forms of prejudice including anti-Semitism is still a place for Jewish people."
Activists are frustrated people who have made abusive comments in the past have been allowed back into the party after suspensions.
In 2014, Vicki Kirby - then a candidate in Woking - was suspended after tweeting that Jews had "big noses" and suggesting Hitler was a "Zionist God". She was later reinstated, becoming the vice-chair of her local party, before being suspended again.
Labour leader Mr Corbyn has repeatedly condemned anti-Semitism.
A party spokeswoman said: "We welcome the contributions of Labour's affiliates and members in this important debate. Rule changes can be submitted to Labour's annual conference where they are democratically agreed by delegates."
Among the local Labour parties that will consider the motion are Hornsey and Wood Green, Tottenham, Hackney North, Hendon, Hertsmere and Sheffield Hallam.