Deputy leader Tom Watson (pictured above) made the pledge following a recent wave in claims of anti-Semitism within the party but he also denied Labour was in crisis.
Former-London mayor Ken Livingstone (pictured below), a close ally of leader Jeremy Corbyn, was suspended yesterday after he claimed Adolf Hitler supported the campaign for a Jewish state.
Mr Livingstone was trying to defend Bradford West MP Naz Shah who was suspended on Wednesday pending an investigation into controversial material she posted on social media proir to becoming an MP.
Speaking with Premier Christian Radio, Dr Jane Clements from the Council for Christians and Jews, said: "The zero-tollerance [approach] is a brilliant idea and [so is] people realising when what they have said over-steps the mark.
"I think it'll be great if people have a little bit more care and concern about they've said about people from other groups.
"What all the events in the headlines have shown over the last few days is that we need to clearer as to what is anti-Semitism [and] what is legitimate criticism of Israel and how these things are linked but seperate."
Mr Watson told the BBC Radio 4 Today programme: "What Ken Livingstone said yesterday was vile, offensive and crass and it was absolutely right that Jeremy suspended him.
"To link Hitler and Zionism in the way he did must have been done to create offence."
It seems the way Labour candidates are chosen could change as the party re-evaluates it's own structures.
Mr Watson added he and Mr Corbyn had "both been talking to representatives of the Jewish community to look at whether Labour's own structures can be improved to make sure that we send a very clear signal to people in our party that we will have a zero-tolerance approach to anti-Semitism".
Jonathan Arkush, president of the Board of Deputies of British Jews, told Today: "It was much more than offensive language. Ken Livingstone actually said that Hitler was some sort of Zionist.
"I also want Jeremy Corbyn finally to say that his own meetings with anti-Semites in the past, before he became leader, were inappropriate and should not be repeated."