Vivian Wineman, president of the Board of Deputies, defended its position on Israel in a meeting with critics in London on Wednesday night.
It was attended by 90 of the more than 1,000 signatories of an online petition calling on the Board to declare explicit support for a two-state solution to the Israeli-Palestinian conflict.
The protest followed the Board's rejection in January of a resolution backing two states and was organised by Hannah Weisfeld, who is fronting moves to set up a new Israel campaign group similar to the American J Street.
Mr Wineman said the Board was "not opposed" to the idea of a two-state solution but deputies did not want to pass resolutions about policies the Israeli government should be following.
But Naomi Wayne told him: "The message sent to the world was that the Board did not support a two-state solution."
Anthony Tricot, an under-35 deputy, said the Board was "completely unrepresentative of the wider community" and he thought the average deputy was more likely to be right-wing.
Mr Wineman disputed this although he conceded that right-wingers on the Board "do make a lot of noise".
Barend Velleman said that as a result of the failure of the Board to pass a resolution, some synagogues were reconsidering their affiliation to it.
The Board's senior vice-president, Jonathan Arkush, said: "We accept you can be supportive of Israel and critical of its government."