The comments come as a former chief rabbi says Jews are asking whether Britain is a safe place to bring up their children.
The former prime minister called for a comprehensive strategy against anti-Semitism in a London speech, saying it was "not just a procedural issue but about the soul of the party".
"The sore that exists and the harm that has been done, and the hurt it has caused, has got to be undone."
He made the speech in advance of a meeting by Labour's National Executive Committee over whether to adopt the IHRA definition, and hours after rabbi Lord Sacks launched a renewed attack on Jeremy Corbyn over anti-Semitism.
The former chief rabbi told BBC1's Andrew Marr programme that unless the Labour leader "expresses clear remorse" for comments made about British Zionists in 2013, he posed "as great a danger as Enoch Powell".
"Jews have been in Britain since 1656, I know of no other occasion in these 362 years when Jews - the majority of our community - are asking 'is this country safe to bring up our children'," said Lord Sacks.
"Anyone who uses the term Zionist loosely, without great care, is in danger of engulfing Britain in the kind of flames of hatred that have reappeared throughout Europe, and is massively irresponsible.
"There is danger that Jeremy Corbyn may one day be prime minister, he is the leader of Her Majesty's opposition.
"I'm afraid that until he expresses clear remorse for what he has said and what his party has done to its Jewish sympathisers as well as its Jewish MPs, then he is as great a danger as Enoch Powell was."
In another interview with Andrew Marr, shadow chancellor John McDonnell invited Lord Sacks to speak further with Mr Corbyn.
He said he believed "all sides would be satisfied" with Labour's planned proposals for a new definition and that the party would "resolve this matter" and "move on".
"I think when you sit down with Jeremy you will find you are virtually on the same page on many of these issues," he said.
"You'll be able to work together to tackle this issue of anti-Semitism in our society, which we acknowledge exists and we've got to tackle together."
Mr McDonnell has expressed his concerns about the prospect of the Labour party splitting.
In an interview with the New Statesman, Mr McDonnell said he wanted to avoid a split "at all costs" and address the ongoing anti-Semitism scandal "as quickly as possible".