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"I've done public meetings all over London and in some cases all people want to talk about is what I'll do to clamp down on anti-Semitism," he added in the emailed statement.
"There is a sense of fear and anxiety. It's completely wrong that the Labour party tolerates this. They need to take this issue more seriously and show they will take action."
His remarks follow the suspension of former Labour London mayor Ken Livingstone over his comments on Hitler and Israel.
Livingstone waded into a row on anti-Semitism this week sparked by (now-suspended) Labour MP Naz Shah's social media posts suggesting Israel should be relocated to America.
But the veteran Labour politician became the target of blistering criticism from politicians of all major political parties after he defended Shah and told BBC Radio London that Hitler "was supporting Zionism" in 1932," before he went made and ended up killing six million Jews."
The former mayor was subsequently suspended by the Labour Party on Thursday afternoon for "bringing the [Labour] party into disrepute."
This all comes less than a week before the Mayor of London elections on May 5.
Sadiq Khan's, Labour's Mayor of London candidate, is comfortably beating Conservative opponent Zac Goldsmith in the poll. Khan condemned Livingstone's comments prior to his suspension - but the ongoing row threatens to harm his campaign.
Ken Livingstone's comments are appalling and inexcusable. There must be no place for this in our Party.
- Sadiq Khan MP (@SadiqKhan) April 28, 2016
Sadiq Khan's camp did not immediately respond to a request for comment about Ken Livingstone's remarks.
Racism has become an unexpected issue in the bitterly fought 2016 London mayoral election. Goldsmith has previously attacked Khan's judgment for "sharing a platform" with extremists, with Khan camp's countering that Goldsmith's comments amount to dog-whistle racism intended to play on prejudices around Khan's Muslim faith. Goldsmith denies this.