In a strongly worded statement, the Ibrox club insisted there was no chance it will fold or run up crippling debts and would defend their case "vigorously" if it proceeded to court.
Rangers admitted they disputed the claim, which arose from a failure to pay invoices issued by the Singapore-based Orlit Enterprises. The club claimed not all invoices submitted were "legitimate".
They criticised some reports and bloggers who had posted details of the case, adding: "Despite what some over-excited but desperately ill-informed bloggers claim, there is no threat of this club being closed. That is downright malicious and ludicrous."
The club's owners had previously stated it was debt free when raising more than £22 million while floating on the AIM stock exchange.
The invoices are understood to be linked to Orlit's involvement in introducing investors to provide seed capital to buy the club from the administrators and secure the June 2012 payroll.
Orlit is said to have taken action because there was no satisfactory answer to the non-payment and is expected to seek the winding-up of The Rangers Football Club Limited (RFCL), formerly Sevco Scotland Ltd.
The club said the sums sought were "insignificant" and that an "agreement has been reached subject to the necessary paperwork".
They admitted they had been in dispute with Orlit, but had now reached an agreement, adding: "Only the wording, which would put this matter to rest once and for all, has still to be signed off." If Orlit planned to instruct lawyers to go to court, then the club would "defend its position vigorously".
The statement added: "We are absolutely convinced we would win, but we did think it would be better to avoid giving our many detractors another bar with which to beat us over the head. That is why we made an offer to settle, but we now find we are still being harassed.
"The thought process seems to be that if we have £22 million [from the share offer] we should just pay up. Bizarre. Why should we? Of course we can pay the amount demanded, but it is ridiculous to hand over more than is due. The money belongs to Rangers and we will not give it out to anyone who comes along with invented invoices.
"That would be reckless in the extreme and suggest nothing has been understood from the past when Rangers were in effect mugged by money-grabbers.
"We are here to make sure that does not happen again. We do pay our bills on time and we have always been prepared to pay this one."
The statement went on: "Rangers are no longer soft touches. We will not bow to or run from bullies and we will not be pressured into handing out even £1 if it is not merited."
Orlit – run by businessman Chan Fook Meng, an associate of Rangers chief executive Charles Green – was unavailable for comment.
Rangers entered administration a year ago next week, after Craig Whyte bought Sir David Murray's 85.6% shareholding for £1.
Administrators Duff & Phelps negotiated a sale of the club's assets to a consortium led by Mr Green. for £5.5m. It was thought at the time this was in the form of a loan, to be repaid by the club with interest by 2020.