Rangers chief executive Charles Green has urged fans to back his consortium instead of resorting to what he described as attempts to undermine their rescue plans for the club.
A crowd of around 1,500 staged a protest against the new regime outside Ibrox on Wednesday night, led by former defender John Brown.
Brown, who has urged Light Blues supporters not to renew season-tickets, plans to lead a fans' buyout of the Sevco group, who purchased the business and assets of Rangers for £5.5million earlier this month.
Green told BBC Scotland: "It's not right that a proportion of Rangers fans continue to attack my consortium and try to undermine our rescue plans.
"It's not right that every two weeks a Mel Gibson appears, delivers a Braveheart statement, then doesn't deliver anything."
Green faces the prospect of relaunching newco Rangers in the Scottish Football League, with his application for entry to the Scottish Premier League doomed to failure.
Seven of the 12 SPL clubs have now publicly stated plans to reject the bid at next week's formal vote, which requires an 8-4 majority.
Reports yesterday claimed plans are being put in place that would see Rangers relegated from the SPL to the Irn-Bru First Division with immediate effect, rather than start from scratch in Division Three.
Asked for his views on the proposals, Green added: "Did you refuse to pay the price of membership of your golf club?
"My opinion upon right or wrong doesn't matter.
"We will continue to work to ensure Rangers play football next season and that we can look everyone in the eye."
The Rangers Fans Fighting Fund will seek supporters' views on the issue.
A statement read: "In the interests of sporting integrity, and mindful of the manner in which other Scottish clubs have sought the opinion of their supporters, the RFFF is to canvass Rangers fans - using the massive database of Ibrox season ticket holders - and ask them their collective opinion on the current circumstances.
"The fans will be asked for their preference of the three options that we see open, namely: that Rangers FC should apply to join the SFL 1st Division next season (which may include possible sanctions); that Rangers FC should apply to join the SFL 1st Division next season (with no sanctions); or that Rangers FC should apply to join the SFL 3rd Division next season (with no sanctions)."
A statement from Hibs - one of the clubs who will vote against newco Rangers' SPL application - read: "If, as a result of the vote on 4 July, the Rangers newco is not voted into the SPL then it will be for other bodies to decide if and at what level Rangers might be accommodated within Scottish football."
Meanwhile, Rangers have clarified Direct Debit arrangements for season-ticket holders opting against renewal, telling fans: "All season tickets which were paid by Direct Debit last year were automatically lodged again as they are held in one batch.
"This does not take payment and merely sets up the instruction for the full batch.
"As season holders have advised us that they wish to cancel their Direct Debit, their seat is cancelled in our ticketing system and, when the payment instruction runs to take payment, all those who have advised the club of their wish to cancel will be excluded from the payment run.
"Whilst we appreciate that this is far from an ideal situation, we hope that all our season-ticket holders recognise that the current transition period is challenging operationally and would ask for your continued patience."