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It has been a "dreadful week" for Labour, shadow chancellor John McDonnell said as he called on suspended member Ken Livingstone to apologise for claiming Hitler "supported Zionism".
In an interview, Mr McDonnell said the controversy over alleged anti-Semitism in the party had damaged its election chances.
He said he would not rule out that the row was a plot to undermine the leadership - but said what mattered was ridding the party of any instances of racism.
Labour leader Jeremy Corbyn has said he is determined to root out racism in all forms in the party amid accusations of anti-Semitism within the party.
It follows the suspension of Bradford West MP Naz Shah for an antisemitic Facebook post and Ken Livingstone's remarks that linked Hitler to Zionism.
In an interview with the Guardian, Mr Corbyn said: “Labour is an anti-racist party to its core and has a long and proud history of standing against racism, including antisemitism."
Mr Corbyn has appointed former head of rights group, Liberty, Shami Chakrabarti, to lead an independent inquiry into antisemitism within his party.
As part of this Chakrabarti will talk to members Jewish community to establish how it can best tackle antisemitism and other forms of discrimination and racism.
Labour's leadership has maintained a diplomatic silence of sorts today in the row over anti-Semitism within its ranks, but the party has found itself unable to fully draw a line under events.
Labour Peer Lord Dubs told ITV News the leadership had been slow to respond to the issue, and that the row was a disaster for the party.
ITV News Political Correspondent Libby Wiener reports.
Labour is stepping up efforts to "clarify policies, procedures, and the rules" over how it tackles anti-Semitism, according to the shadow education secretary.
Labour MP Lucy Powell told ITV News the party needed to be "absolutely clear" it had "zero tolerance" for anti-Semitism within its ranks, and that there were a number of investigations ongoing.
Ken Livingstone has refused to comment on the anti-Semitism row that has rocked the Labour party.
The former Mayor of London was suspended by the party pending an investigation following comments he made while attempting to defend MP Naz Shah, who was also suspended for alleged anti-Semitism.
Livingstone told reporters while walking his dog Coco: "Nothing, not a word will come from my lips. I'm going to spend the rest of the week gardening."
He added that anyone who wants to hear his views will need to listen to his radio show on Saturday.
Shadow home secretary Andy Burnham has said Labour should act quicker to deal with anti-semitic comments.
Ken Livingstone has been suspended by Labour for "bringing the party into disrepute" amid an anti-Semitism row.
"These allegations, when they are surfacing, have not been dealt with properly and quickly enough. They need to be dealt with much more speedily in the future," Mr Burnham told BBC1's Question Time.
Labour MP Wes Streeting, the vice chairman of the all-party parliamentary group against anti-Semitism, warned that inaction by the leadership was damaging the party's reputation.
"What has been most frustrating when it comes to dealing with individual examples of anti-Semitism in the Labour Party has been the flat-footed response of the Labour Party which has given the impression that we are apathetic to tackling anti-Semitism or indifferent," he said.
"This ostrich strategy cannot be allowed to continue. Our credentials as a party of tackling racism in all its forms is taking a battering."
Former shadow home secretary Yvette Cooper has said that suspensions are not enough and the Labour party needs an "action plan" to tackle alleged anti-Semitism within its ranks.
Speaking to Channel 4 news she said: "The Labour Party needs to do more than simply to have suspensions of people who have been saying anti-Semitic things.
"We've actually got to have an action plan to deal with this in order to have strong processes so that there is swift action because you can never tolerate that kind of discrimination in the party."
Labour leader Jeremy Corbyn has denied that Labour is in crisis after prominent party member Ken Livingstone was suspended for "bringing the party into disrepute" over comments about Hitler.
Speaking to the BBC he said: "It's not a crisis. There's no crisis. Where there is any racism in the party it will be dealt with and rooted out. I have been an anti-racist campaigner all my life.
"There is not a problem. We are totally opposed to anti-Semitism in any form within the party. The very small number of cases that have been brought to our attention have been dealt with swiftly and immediately, and they will be."
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