The announcement means chief executive Craig Mather, finance director Brian Stockbridge and director Bryan Smart will stay on the board, at least until the AGM.
The announcement also suggests that none of the group of disgruntled shareholders who called for a general meeting will join the board in the short term, although that could change at the annual meeting.
A Rangers statement to the London Stock Exchange stated that the board had been continuing talks with representatives of that group, who they call the "requisitioners".
The statement added: "The company can confirm that the requisitioners have withdrawn the requisition which put forward resolutions for the removal of Craig Mather, Brian Stockbridge and Bryan Smart as directors of the company and for the appointment Frank Blin and Paul Murray as non-executive directors of the company on the condition that the company convenes its annual general meeting to be held no later than 31 October 2013.
"The company confirms that all of the current directors remain in office and that it is not appointing any additional directors save that as previously announced, the company confirms that it continues to actively seek to appoint a new chairman."
Rangers had last week announced that they had reached an agreement that would see Blin, Murray, Sandy Easdale and John McClelland join a new nine-man board.
However, the disgruntled shareholders, who have been guided by Clyde Blowers chairman Jim McColl, subsequently denied the club's claim that they had agreed to a vote of confidence in the current board.
With no compromise being reached, the make-up of the board now looks set to be resolved at the club's AGM, with the only concession from the group making the demands being that the club is spared the expense of convening a separate meeting.