Mark Warburton has called on Rangers to answer questions put to them by the League Managers Association as he reiterated his position that he did not resign from the club.
In a joint statement with David Weir and Frank McParland, the deposed Rangers management team expressed their surprise that the club had not addressed the questions posed to them.
Rangers announced on Friday they had accepted the trio's resignations and Graeme Murty took the team during Sunday's William Hill Scottish Cup win over Morton.
The statement, released by the LMA, read: "Much has been said over the last few days relating to our departure from Rangers Football Club.
"At this stage, for legal reasons, it is inappropriate for us to comment in any great detail on our departure from the club.
"However, given that the club has seen fit to make detailed public statements, it is important that we should clarify certain matters and as such we would like to formally place on record, that at no stage did we resign from our positions at Rangers.
"It is a matter of surprise to us, and to the League Managers Association (LMA), which is advising all three of us, that despite its detailed public statements, the club has not answered key questions put to it by the LMA, in writing, requesting an explanation of why it suggested that we resigned from our positions."
Rangers released a statement on Friday that claimed manager Warburton, assistant Weir and head of recruitment McParland had come to an agreement to leave the club via their joint representative.
Chairman Dave King followed that up on Saturday with a lengthy update which criticised Warburton for his response to boardroom scrutiny and accused him of a lack of commitment to the club.
King claimed that after a meeting, their agent "subsequently offered that Mark, David and Frank would resign with immediate effect without compensation as long as the club, in turn, agreed to waive compensation from any new club that they signed for.
"After discussion the board accepted this offer and employment was immediately terminated. In order for us to achieve our ambitions we need employees that, like your board members, will always put Rangers first.
"While we were dealing with the admin and press releases relating to the resignation the agent again contacted us and asked to defer the resignation until the management had secured a new club.
"I assume that the new deal had somehow collapsed at the last minute.
"The board met to consider this request but resolved to hold them to the original agreement."
The issue looks set to run and run and could end up in the courts given the distance between both versions of events.
In the meantime, Rangers are searching for a new management team, which could include a director of football, while Warburton, Weir and McParland could be in limbo until the legal issues are settled.
They took the opportunity to thank players and fans for their support during their time with the club.
Their statement added: "For all three of us, it was an absolute privilege to be given the opportunity to work at a club that is so rich in tradition and history.
"It was an honour to be given the responsibility of returning the club to the top tier of Scottish football and we are very proud to have played our part in successfully securing promotion back to the Scottish Premiership.
"Winning the Petrofac Scottish Challenge Cup and beating Celtic, in a memorable semi-final to reach the Scottish Cup Final, are experiences we will never forget.
"We sincerely thank the Rangers fans for their unwavering passion and dedication. We had the good fortune to meet so many outstanding individuals and supporters of the club and we will always value their words of encouragement. We wish them great success for the seasons ahead.
"The current group of players, together with the staff at the training ground and Ibrox, have borne the huge weight of responsibility of taking a massive club back to the top flight. They should be proud of their togetherness and their work ethic.
"It has been a pleasure to work with them, and we would like to thank each and every one of them for their commitment and contribution."