Rangers have called for the suspension of SPFL chief executive Neil Doncaster and an investigation into the league body's handling of the members ballot.
The club, who also want SPFL legal adviser Rod McKenzie removed while a probe is held, claim they have received evidence of a lack of "fair play".
Rangers say they will not be "bullied into silence" over these concerns.
SPFL chairman Murdoch MacLennan has told interim Rangers chairman Douglas Park to prove or withdraw the claims.
MacLennan said: "It is extremely concerning that Rangers have chosen to make a number of very serious allegations against the SPFL.
"In the often-heated atmosphere of Scottish football, rumour and misinformation can very quickly reach fever-point. However, allegations of a lack of even-handedness and fair play go to the very integrity of the league.
"I will be writing to Mr Park asking him to urgently communicate any and all information he possesses."
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Rangers had said they were given evidence by a whistleblower that raised "serious concerns" over the voting process.
And they claimed Doncaster tried to silence Park's attempts to discuss the matter.
"We believe it is in the interests of all Scottish clubs and supporters that the evidence, which is alarming, be addressed as quickly as possible," the club's statement said.
"The voting debacle and the evidence we possess raise serious questions concerning the corporate governance of the SPFL."
The outcome of the SPFL's resolution on ending the lower-league season rests on Championship side Dundee, who have yet to vote despite the league's requested cut-off of 1700 BST on Friday.
Shortly after that deadline, the SPFL released the figures so far, which showed a sufficient number of teams in the Premiership and Leagues One and Two backed the proposal while three of the 42 member clubs had yet to vote.
If passed, the motion would also lead to the Premiership being declared on the same points-per-game basis if the SPFL board determines the remaining fixtures cannot be played.
Rangers' their counter resolution - whereby prize money would be released now with no leagues declared - was rejected as "ineffective" by the SPFL on Friday.
That led to Rangers saying they had received "numerous reports" from Scottish clubs of attempts by the SPFL to "coerce and bully" them into accepting the league body's own proposal.
Park said: "The lack of leadership and responsibility from the SPFL as a members' organisation has shocked me. Crucial decisions are being made on the issues of promotion and relegation behind closed doors and without proper time for consideration or debate.
"All we ask for is equality and respect. In the past few days, we have become alarmed at a seeming lack of even-handedness and fair play from the SPFL. This is surely unacceptable and, if substantiated, must be remedied.
"Other member clubs, who have seen the evidence we hold, share our concerns. We call for the suspension of the SPFL's chief executive Neil Doncaster and its legal adviser Rod McKenzie while an independent investigation is conducted."