Chief executive Craig Mather and non-executive director Bryan Smart both resigned last week, leaving Brian Stockbridge and James Easdale as the only current members of the Ibrox board.
Days earlier, former oldco director Paul Murray won a courtroom battle to force the postponement of the club's annual general meeting, which was set to take place on Thursday, after the board attempted to block a motion for the election of potential new directors.
A statement on behalf of the Rangers Supporters Association, Rangers Supporters Assembly and the Rangers Supporters Trust read: "The events of the past week have caused further anxiety among Rangers fans and we now call upon the club and their advisers, Daniel Stewart, to clarify a few matters as quickly as possible.
"The next few weeks are a critical period for us all and, after what we've been through, we need some measure of reassurance that there will be stability soon.
"Firstly, when will the club's AGM be held? The delay resulting from the Court of Session ruling last Monday, followed by the resignations of Craig Mather and Bryan Smart, leaves the current Board of Directors extremely vulnerable.
"Whilst we welcome the words of reassurance from Brian Stockbridge that the club's finances are stable and operations will continue as normal, we feel it is imperative that the AGM is convened as a matter of urgency.
"Secondly, given the level of concern among fans regarding the ownership and finances of the club over the recent past, and the various investigations that have been undertaken, we feel it is vitally important that the individuals that are behind both Blue Pitch Holdings and Margarita Holdings are made known to remove any doubt that there are connections to either Craig Whyte, Imran Ahmad or Charles Green.
"Both Walter Smith and Ally McCoist have spoken of the need to "cleanse" the club of all the rumour, speculation and innuendo.
"The identity of the individuals behind these two shareholder groups is a significant part of that "cleansing" process.
"Thirdly, we call upon the Easdale brothers to clarify their position going forward.
"They are now in a prominent position, both in terms of their shareholding and influence on the Board, and it is important that fans understand their view of the future structure of the Board and the running of the club.
"The club has adopted a very defensive position recently in efforts to rebuff allegations and clarify misinformation.
"Now is the time to take a positive stance and provide the fans with the clarity and factual information we request and to take the lead in shaping the way forward."