Mr Davis, responding to the "unwarranted and egregious attack", said Mr Arkush's position was "untenable". He said JLC members "may feel that they can no longer provide ongoing financial support for the Board while being subjected to this sort of attack by the senior vice-president of the institution".
Mr Wineman, speaking after the meeting, said that it was "unhelpful and incorrect" to suggest the JLC was unaccountable.
"To make totally unfounded implications of possible impropriety is not acceptable". The JLC and Board "work closely together".
Mr Arkush spoke out after complaints from deputies that the JLC was "taking over" the political role of the Board, although his intervention led to accusations that he was undermining Board president Vivian Wineman, who also acts as chairman of the JLC council.
Deputies have long harboured suspicions about the ambitions of the JLC since its creation in 2003, but Mr Davis and Mr Wineman have tried to soothe tensions by insisting the two organisations were partners rather than rivals.
Mr Arkush's outburst was prompted by last month's meeting of communal leaders with Prime Minister David Cameron. Although Mr Wineman led the delegation, most of the other participants were from the JLC.
Mr Arkush - who sits on a liaison committee to improve relations between the Board and the JLC as well as a JLC committee overseeing its political work - said the time had come to raise "serious questions" about the JLC's remit and expenditure, which had "soared" into several hundred thousand pounds a year.
He suggested some organisations had been put under pressure to remain on the JLC and that the Manchester and Leeds Representative Councils had received money when they joined.
The JLC comprises the heads of more than 20 communal organisations plus a number of prominent individuals. Its budget, which was around £450,000 in 2010, is mainly funded by subscriptions from member organisations, plus £5,000 gifts from individuals and grants for one-off projects.
David Arnold, president of the Manchester Rep Council at the time it joined the JLC, denied that it had received any payment from the JLC.
Hilton Lorie, president of Leeds Rep Council, which joined last month, said it had "received no money whatsoever from the JLC".
