The Union of Fans has released a statement stating they want the club to make an iron-clad promise not to put the stadium and training ground up as security to be used to secure cash investment.
It comes after former director Dave King met with the new League One champions' unpopular ruling regime last week in a bid to address lingering concerns about the club's financial state following last year's £14.4million loss.
The board, in a statement released on Saturday, promised the South African-based businessman it was determined to place Rangers back at the forefront of Scottish football as well as insisting it had "no intention" of using Ibrox or Murray Park for security.
But in its own statement, the fans group said: "Although pleased that the [board] have made a commitment not to raise finance, or take out any type of security, on Ibrox or Auchenhowie, we are disappointed that they have refused to make this as unequivocal as we would have expected. 'We have no plans' does not engender the same confidence as 'we will not'."
King released his own statement on Monday which toned down an increasingly bitter war of words.
In it, he said he would give the board 30 days to complete Graham Wallace's 120-day review of the club but warned that as the directors of a public company, they were bound to stick to the promises they made.
And the fans' group backed the Castlemilk-born multi-millionaire's stance, stating: "Clearly the board's position has changed over the weekend, from one where we had no clear sight of their strategy with regard to moving the club forward, to one where they have now committed to fans and shareholders to implement the funding plan we believed was required.
"This plan, if properly executed, should allow the club to compete both domestically and in Europe in the medium term. We are pleased that they are no longer considering the massive scaling back of club operations that would have been required, both on and off the park, under their previously assumed but never communicated strategy.
"We also note that they have confirmed that they do require further investment as a matter of some urgency. We expect significant amounts of that investment to come from a united fan investment vehicle, including Dave King.
"Having secured these binding, public commitments from the board, through Dave King, we are now prepared to wait for the publication of the business review from Graham Wallace within the next 30 days.
"We expect it to fully reflect the promises made by the board in their last statement and we are, reluctantly given previous experience, relying on them to fulfil those promises. We expect them to produce a coherent vision and detailed plan of how they will fund it."
King had suggested that if the fans wanted a greater say in how Rangers were being run, they should set up a trust which would collect season-ticket cash and drip feed it to the club.
Now the Union of Fans has confirmed it is ready to launch that scheme in the coming days.
The group's statement added: "We will be continuing with plans to set up a Season Ticket Trust. We are determined to be in a position to provide it as an option, if required, and will continue to update the supporters on our progress on a regular basis. We expect to engage with legal advisers and trustees as early as next week."