Mr Dismore said that the former mayor had "always had a difficult relationship with the Jewish community" , but added that the assumption about Jews not supporting the party was incorrect.
He said that while Mr Livingstone was entitled to his views about Israel, "he certainly has no right to translate those view into a general condemnation of the Jewish community.
"The words Jewish, Israeli, and Zionist, are not interchangeable."
Mr Dismore said that now, as in the past, over issues such as Mr Livingstone's warm welcome of Sheikh Yusuf al-Qaradawi, he had "significant differences with him on the Jewish community".
But he promised to hold him to account if he was elected, and still urged Jewish voters to back Labour at the elections in May, noting that Mr Livingstone, as mayor, would have "no say in foreign policy".
He said that he was willing to share a platform with Mr Livingstone because he had no dispute with him over the policy issues. "Despite everything I hope that he is elected because that is the best guarantee of delivering on fares, policing, housing and cost of living, which I think Jewish people would like to see. The problem is of course that the personality gets in the way."
Mr Dismore said he belived Ed Miliband, the Labour Party leader, should not comment on Mr Livingstone's attitude toward the Jewish community.
"It's a London Labour party issue," he said. "Ken has been adopted as a candidate and I don't really think that constitutionally Ed has really got anything he can say about it."
