Labour's shadow leader of the Commons Angela Eagle said Unite general secretary Len McCluskey was entitled to express his own opinion on calling for the internal inquiry on Falkirk to be released but it was Ed Miliband who would decide what should be done.
Ms Eagle told BBC Radio 4's Today programme: "Len McCluskey can have an opinion on that, but it is the internal party Labour structures which will decide on how we protect the integrity of our rules.
She added: "We will not tolerate the kind of behaviour we have seen in Falkirk, whoever is responsible for it. There is sufficient evidence of misbehaviour amongst particular individuals up in Falkirk to justify the action that the leader of the Labour Party took yesterday."
Responding to Ms Eagle's comments, Labour's former general secretary Peter Watt - who held the post from 2005 to 2007 - said on Twitter:
If Labour attempts to blame #Falkirk just on 'particular individuals' rather than accepting institutional problem it will be a disgrace.
Labour leader Ed Miliband has turned on the trade union Unite - his biggest financial backer - whose votes helped him become leader.
Tom Watson has announced his resignation from the shadow cabinet, amid a row about the influence of the union Unite on the Labour party.