The union, an organisation comprising four supporters' groups, revealed they have been locked in talks with the Glasgow club for nearly a fortnight.
They wanted legally-binding guarantees over the SPFL League One champions' main assets - Ibrox Stadium and the Murray Park training ground.
But the body rejected the statement posted on the official club website on Sunday night because they felt "several misleading statements are made within it".
And the union has now accused the board of being "disingenuous" over the future of the stadium - and of looking to sell the training ground to generate cash.
A UoF statement read: "We were seeking written guarantees over both Ibrox and Murray Park. The board removed all reference to Murray Park. This was not an oversight. They are explicitly refusing to include Murray Park in any undertaking.
"We believe this is because the board are actively looking to sell this vital club asset due to their failure to so far secure enough funds to see the club through the current season."
The Union has also insisted that repeated club statements over the future of Ibrox are "disingenuous" and do not go far enough to protect it.
He said: "Despite their attempts to claim otherwise, it has never been their position to give any kind of legally-binding guarantee over Ibrox and they still have not done so.
"This most recent statement - on behalf of the so-called 'Football Board' not the plc board - has crucially not been released to the stock exchange and therefore reduces the chance of shareholder action should they go back on their word.
"Their statement is a slap in the face for the thousands of fans who have given up long cherished seats attempting to get this board to guarantee the future of our club's home.
"The board claim that they are 'committed to protecting the assets of the club'. Currently the club has four main assets. Two of those, Edmiston House and the Albion Car Park, have already been used as security for crisis loans due to financial mismanagement.
"The board continues to refuse to give any legally binding safeguard over Ibrox and we believe they are actively looking at a sale and leaseback of Murray Park - a vital asset if we are ever to properly develop our own talent. They have shown no commitment to protecting the club's assets."
The Union of Fans have also questioned whether Rangers can raise enough money from existing shareholders in a new share issue in September to keep the club afloat.
And they have urged chief executive Graham Wallace to outline how the club, which continues to operate at a significant monthly loss, can get through the 2014/15 campaign.
The statement continued: "The board have lost just under half of the club's season ticket holders due to a complete lack of ability to build trust. Even if those fans were to buy season tickets now, the club still does not have the funds to complete the season."