The Rangers board claimed an attempt to install Paul Murray, Malcolm Murray, Scott Murdoch and Alex Wilson, in a proposed vote at the club's annual general meeting on October 24, was ''unlikely to be properly constituted under s338 of the Companies Act 2006''.
However, the group seeking change insists it submitted its request in a "perfectly valid" manner.
The row follows an earlier agreement which saw a group of dissenting shareholders, led by Clyde Blowers chairman Jim McColl, drop demands for a general meeting to vote on a resolution to remove chief executive Craig Mather, Brian Stockbridge and Bryan Smart and install Paul Murray and Frank Blin, in return for a guarantee that the club's AGM be held before the end of October. An earlier compromise deal fell through.
Current directors could be voted off at the AGM but the board announced it considered the new resolution invalid and "vexatious" because no amendment to the terms of the withdrawal of the original request had been discussed beforehand.
In a statement to the London Stock Exchange, Rangers said: "The board is also concerned that the contents of the proposed resolutions may also be either ineffective or frivolous as any director appointment must comply with the company's articles of association and is subject to prior regulatory approval."
The club also claimed that the request, which was received on Friday, arrived after notice for the AGM had been sent to the printers. The club's annual accounts, which revealed operating losses of £14.4million, were published four days later on Tuesday.
In a statement released to Press Association Sport, a representative of the dissenting shareholders accused the board of being unreasonable and insisted their aim was to strengthen the board with "successful professionals who are lifelong Rangers supporters".
The statement added: "We confirmed to the board that we would meet the reasonable additional costs and expenses of including these nominations in the AGM notice.
"We heard nothing from the board all weekend until their lawyer, Field Fisher Waterhouse, was in contact at lunchtime on Monday requesting a large volume of information to authenticate our notice and to inform us that, in any event, 'the AGM documentation was sent to the printer for printing and posting on Friday'.
"This is despite the fact that we now know that the accounts were not signed until Saturday and the results not announced to AIM until this morning!!
"For the avoidance of doubt we have submitted our notice using a perfectly valid legal process.
"The process of authenticating the notice could have been discussed at any time over the weekend and the process of printing and posting could have been adjusted at any time especially given the fact that we agreed to meet the additional costs.
"Since yesterday we have provided all the relevant authenticating materials we believe are required. In addition we have even offered to pay for an additional document to be sent to shareholders after the main notice has been posted. The board and their advisers have blocked these offers."
The statement continued: "In our opinion the board has acted in a wholly unreasonable fashion by denying the shareholders the right to vote on new directors who would undoubtedly strengthen the board.
"At all times we have sought to minimise the cost and disruption to the club from this process. We agreed to combine the AGM and GM and we agreed to try and find a compromise with the board on appointments.
"The current directors and their advisers blocked those moves and are now blocking this latest attempt to strengthen the board.
"It is extremely disappointing and frustrating that matters have come to this point. You have to ask the question why this board is so hell-bent on denying the shareholders a democratic vote on who they want as directors at the AGM?"
The group also noted Rangers' announcement that Strand Hanson, who they accused of blocking the compromise deal that would have ensured no board members would have been removed before the AGM, had been replaced as nominated advisors by Daniel Stewart, the third firm to fill that role in 10 months.
And they dismissed reports they were considering a sale and leaseback of Ibrox and Murray Park, as well as a staff cull, as "wholly inaccurate".
Malcolm Murray is a former chairman of Rangers who left the board in July following a fractious relationship with former chief executive Charles Green. Paul Murray is a former director of oldco Rangers who was removed from the board shortly after Craig Whyte's takeover, which he had opposed.
- Investment & Company Information