Lord Falconer has said the row over anti-Semitism within Labour could pose an “existential threat” to the party.
Not dealing with the issue could erode the party’s effectiveness as a political force, the ex-minister told the BBC.
The Labour peer has come under pressure to reject an offer from Labour to head an inquiry into anti-Semitism claims.
The Equalities and Human Rights Commission is considering launching a formal investigation into the party.
Speaking to BBC Radio 4’s World At One, Lord Falconer said he would not take up the role until the rights watchdog decides how it will proceed.
The EHRC said earlier this month that the Labour Party may have unlawfully discriminated against Jewish people.
The watchdog is asking the party to work with it to improve its processes, before deciding whether to launch a formal probe.
Lord Falconer also defended the idea that a party review into anti-Semitism within Labour could be carried out by a party member.
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Some Labour MPs have called for someone from outside the party to lead the probe.
“It may be that some people would think any member of the Labour Party would not be a sound person to do that,” he said.
“I don’t think that’s right, I think it would have been OK for a Labour Party person to do it, because I’m completely independent of the leadership.
“I think the way that we as a party are being affected, because we are characterised as an anti-Semitic party, is hugely damaging,” he added.
“There does need to be both a huge searchlight on what we’re doing in relation to our disciplinary process – and there needs to be something that’s ongoing, in order to ensure that we stick by an effective disciplinary procedure.”