HBOS is subject to a takeover by Lloyds TSB
Lord Mandelson has been accused of bully-boy tactics after it was claimed his lawyers sent a threatening letter to those against the HBOS merger.
Lawyers for the business secretary invited the Scotland-based Merger Action Group to end its protest.
MSPs Alex Neil and Margo MacDonald said the move was "extraordinary".
But the Department for Business, Enterprise and Regulatory Reform (Berr) said the offer had been aimed at saving the group legal costs.
The Merger Action Group (MAG) was formed to mount a last-ditch legal challenge to the deal involving Lloyds TSB and HBOS.
It is due to have its case heard on Monday at the Competition Appeal Tribunal (CAT) - a specialist legal body whose function is to decide appeals on competition issues.
MAG claims that Lord Mandelson's decision to allow the merger to go ahead without referring it to the Competition Commission was unlawful.
In a statement on Saturday, SNP MSP Mr Neil and Independent MSP Ms MacDonald said the letter had threatened MAG's six key members for legal costs unless they halted their court action.
Ms MacDonald added: "I find it breath-taking that a group of responsible people whose only motive in taking this legal action is what best serves the public interest can be subjected to such threats and intimidation by a member of the UK Government."
A spokeswoman for the Department of Business confirmed that lawyers had written to MAG offering them the opportunity to withdraw their case "in light of the strength of evidence against it".
She added: "The letter was intended to give the appellants a chance to save costs before pursuing their legal challenge further.
"It was neither an ultimatum nor a threat to individual members."
MAG's legal bid was fast-tracked last week, with the tribunal deciding the challenge would begin on Monday. It is hoped the appeal hearing could be completed by the following day.
Although the case is being heard in London, it will be conducted under Scots Law.
The UK Government overruled competition concerns raised by the Office of Fair Trading when it gave the merger between HBOS and Lloyds TSB the green light.
MAG spokesman, Malcolm Fraser, who is an Edinburgh architect, said the group had declined the offer of Mr Mandelson's lawyers after it was received on Friday.
He added: "We are committed to our cause in the public interest. We are determined it should go through."
Scottish Liberal Democrat leader Tavish Scott, another backer of the legal challenge, said he was interested to find out if Lord Mandelson and Chancellor Alistair Darling were personally aware that the letter had been sent.
An aide to Scotland's First Minister. Alex Salmond, said Lord Mandelson "would do well to leave the tribunal to determine the case".