A "significant and important body of support for Israel" in the Parliamentary Labour Party was highlighted by Ed Miliband when he addressed the Young Norwood current affairs group's annual reception.
In conversation with the Guardian's Michael White, Mr Miliband expressed frustration at the impasse in the Middle East peace process.
He added that winning the support of Jewish voters was important to him.
He criticised the comments made by Labour MP Paul Flynn questioning the loyalty of Britain's first Jewish ambassador to Israel, Matthew Gould, as "totally unacceptable".
Asked by an audience member whether Ken Livingstone's "unsavoury views" rendered him unfit to stand as Labour's candidate in the London mayoral election, Mr Miliband alluded to Mr Livingstone's "inexcusable" clash with Jewish journalist Oliver Finegold in 2005.
Nonetheless, he was "a strong supporter of Ken Livingstone and he will make an excellent mayor. I know from talking to Ken that he would like to rebuild his relationship with the community. He wants to reach out and build bridges."
The event, which raised £14,000 for Norwood, focused largely on issues of banking, bonuses and responsible capitalism.
Mr Miliband described the weekly Prime Minister's questions as a "nightmare. It's a terrible advert for politics and encourages the view that we are a bunch of schoolkids shouting at each other."