"For us to hold this party together things have got to change. There’s almost a sort of crisis for the soul of the Labour Party now," Tom Watson told the BBC's Andrew Marr Show.
"Of course Jeremy needs to understand that if we’re going to be in No10 that he needs to change the Labour Party.
"We have got to eradicate anti-Semitism, anti-Jewish racism in all its forms.
"This week I have had 50 complaints of anti-Semitism from my party colleagues which I shared with Jeremy.
"I think he needs to take a personal lead on examining those cases and, if necessary, recommend to our NEC what has to be done.
"The test for him as leader is to eradicate anti-Semitism. It is not Labour Party members who will be the judge of that, it is the British Jewish community.
"I think he understands now that if he is ever to be prime minister he needs to rebuild that trust."
The 50 cases sent to Jeremy Corbyn by Tom Watson are understood to include:
A person accused of claiming Jews' "double dealing, back stabbing, cheating chilling coldness has always only one outcome".
A person accused of claiming Jews "pervert democracy in the UK" and calling for the Board of Deputies to be a proscribed terror group.
A person accused of describing Hitler as an "illegitimate Rothschild" and saying of the Holocaust "the figures don't add up".
A person accused of claiming "Jews murder people and children".
A person accused of saying of Jewish MPs Ruth Smeeth and Louise Ellman "don’t know what runs through their veins, not human blood".
Allies of Mr Watson claim all the complaints involve people who were members at the time of the comments, and it is currently "unclear" how the cases were resolved and whether those accused were suspended or expelled.
It comes after eight MPs walked out of Labour this week and joined the Independent Group. Over the weekend, several Labour councillors have also quit the party.