King broke the temporary ceasefire which emerged following talks last month when he claimed chairman David Somers had reneged on a promise to publish an ongoing 120-day review of the club's finances before the end of the season-ticket deadline.
He urged fans to withhold season ticket money - an outcome the club have previously admitted threatens their future.
But the board refuted King's allegations and accused him of lying in a bid to ingratiate himself with supporters.
The furore came two days after Rangers launched their season ticket campaign, which sees many fans facing rises of between 15 and 25 per cent, and sets a renewal deadline of May 6.
Many disgruntled fans are awaiting the results of chief executive Graham Wallace's spending review before pledging their cash.
The 120-day period is due to end in the middle of next week and the club promised on March 15 they would publish the results "in the next few weeks, ahead of the season ticket renewal deadline".
That initially prompted King to successfully advise fans groups to delay plans to collate money into a trust fund, to be handed over only when the Rangers board offered securities over Ibrox and Murray Park in return.
But he said on Friday: "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."
South Africa-based King, who lost his £20million investment when oldco Rangers went into liquidation, continued: "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 Rangers board reacted with "astonishment" and criticised King's comments as "disgraceful".
They said: "Mr King makes a number of untrue allegations against the chairman and the board of Rangers Football Club alleging bad faith and false representation.
"The chairman and the board refute all such allegations in the strongest terms and have referred Mr King's statement to the club's legal advisors."
They accused King of ignoring their previous public statement, in which they promised to issue the business review results prior before the season ticket window closed.
The statement added: "This position remains unchanged and Mr King is well aware of this having sought personal confirmation on this matter from the chairman as recently as yesterday.
"The business review period has not yet even ended, as Mr King is well aware, however he has elected to make yet another public statement to serve his own purposes."
Rangers accused King of exaggerating his willingness to invest in the club. The Glasgow-born businessman has stated he would underwrite a share issue of £30-50million to help the League One champions compete with Celtic - but he is not keen to bail out the current regime on their own terms.
The Rangers statement continued: "When the board met Mr King a few weeks ago, he made it clear that he did not want to put another penny into the club and would prefer to see the club using other investors' money.
"The board was therefore surprised, but gave him the benefit of the doubt when, a few days later, Mr King made media comments about a willingness to invest his money into the club. This is an easy statement to make to the media but is contrary to what he told the whole board.
"It is extremely disappointing that Mr King should consider it appropriate to issue this latest statement, clearly designed to unsettle and mislead Rangers fans, on the eve of an important Scottish Cup semi-final match."
However, King will push ahead with plans to set up a bank account for supporters to collate season ticket money, which would only be advanced to the club once conditions are met, including the provision of club property as security.
The move threatens to undermine the current regime - only two weeks ago Somers admitted "material uncertainty" over season ticket income might cast doubt about the club's ability to continue as a going concern.
Rangers' cash reserves fell by more than £17.5million last year and they recently borrowed £1.5million from two shareholders to meet a shortfall.
- Sports & Recreation