Following a meeting with the Ibrox board last month, King stepped back from initial plans by fans to put season ticket money into a trust fund as he advised them to wait for the club to outline their spending plans.
But he has changed his mind - and advised fans not to buy club merchandise - after further talks with chairman David Somers.
Rangers launched their season ticket renewals on Wednesday and set a May 6 deadline. But King claims they will not publish chief executive Graham Wallace's 120-day review - which is due to finish in the middle of next week - until the end of that renewal period.
In a statement, King said of his initial talks: "The board recommitted to issue the business review within the original 120-day deadline and, importantly, committed that the fans will have access to this review prior to advancing funds by way of season ticket renewals.
"Despite strong reservations from fan groups I asked the fans to give the board time to honour this commitment."
King revealed he felt the board were duty-bound to act in good faith and added: "I followed up on this commitment with the board after the recent announcement on season ticket renewals.
"The chairman has advised me that the board will now only issue the review at the end of the season ticket renewal period and it will consequently not be timeously made available to fans.
"Disturbingly, the chairman has advised me that the true intention of the board had always been to delay issuing the review until funds had been largely collected.
"I apologise to all fans for wasting time by lending credibility to the board's false representations. I was wrong to give them the benefit of the doubt. At least we now can no longer have any uncertainty about the governance at the club."
Rangers are understood to be preparing a response that will accuse King of misrepresenting their position.
The club had issued a statement on March 15 stating that King was "reassured by plans to announce the results of the business review and trading update in the next few weeks, ahead of the season ticket renewal deadline".
The new statement from King, who lost his £20million investment when oldco Rangers went into liquidation, continues: "I have hitherto urged restraint in dealing with the board, however due to this extreme act of bad faith I believe that it is vital that fans now withhold season ticket money from this board and similarly refuse to support the club by way of the purchase of replica kit or any other retail product."
The South Africa-based ex-patriot businessman added: "An announcement will shortly be made providing details of a bank account that season ticket money can be paid into as an interim measure. The specific terms and conditions of this account will be made available to fans, including the basis on which funds will be advanced to the club and the basis on which funds will be returned to fans. As a minimum, the board must provide the club property as security against the season ticket money.
"I recognise that fans will have anxiety about 'betraying' the club and the risk of loss of a cherished seat at Ibrox. However, the time has come when the trade-off is a potential loss of a seat against the loss of the club. That would be the real betrayal. This board has lost its right to be dealt with on a good faith basis."
King added that former Rangers captain Richard Gough had agreed to act as a custodian of the bank account and said fan groups could nominate additional members.