The plea came after former oldco Rangers director Dave King warned that failure to reach a workable agreement at the annual general meeting will mean administration is a "distinct possibility".
King held talks with a number of key parties involved in the ongoing boardroom battle but has returned to South Africa saying that "certain influential shareholders are unwilling to compromise" and predicted an "acrimonious" annual general meeting.
Former director Murray and former Rangers chairman Malcolm Murray - as well as allies Alex Wilson and Scott Murdoch - are backed by wealthy businessman McColl and hope to win directorships when the club finally holds an AGM, which must occur before December 31 under stock market rules.
A statement released on behalf of the group, that says it has the backing of 28 percent of shareholders, claims the board - which is comprised only of finance director Brian Stockbridge and non-executive director James Easdale - has failed to reveal who is behind major institutional shareholders Blue Pitch Holdings and Margarita Holdings.
The statement from the group, which took successful legal action against the board to force an AGM vote, read: "Paul Murray had a private conversation with Dave (King) this morning when Dave updated him on his position following the various meetings and calls he has had in the last week.
"For the avoidance of doubt we remain fully supportive of Dave King's involvement in the club going forward.
"As we have been saying for some time, and is evident from Dave King's statement, it is now clear that there are outside influences who are 'pulling the strings' at Ibrox.
"Over the last couple of weeks we have attempted to clarify the identity of who is really behind Blue Pitch Holdings and Margarita Holdings.
"Having now reviewed the information supplied to us by the club we are unable to identify who is really behind these two companies.
"To avoid a further messy and expensive legal process for the club we are now calling upon the board to do the right thing and disclose to everyone who is really in control.
"If the board have any desire to rebuild trust with the fans then, in the interests of transparency and in light of everything that has happened in the last couple of years, surely they must realise that they must do this as soon as possible.
"If they will not disclose this information then all of the stakeholders in Rangers should ask themselves two simple questions: Why will the board not disclose this information? What do the board have to hide?
"This situation can be easily resolved by the board disclosing the necessary information. The fans deserve nothing less. In the meantime we are considering all options to ensure that there is full disclosure."
King revealed he would continue to seek a solution and would not rule out a takeover attempt but he is resigned to a stormy and indecisive AGM.
While the Rangers PLC board only has two directors, Easdale sits on the football club board and claims to control the largest individual shareholding, whether by ownership or proxy.