A nine-year battle between RBS and angry shareholders ended at the High Court on Wednesday as a judge agreed to stop the case.
The majority of the RBS Shareholders Action Group of 9,000 investors have agreed to accept a £200m settlement relating to a £12bn bailout in 2008.
But 13% of shareholders have still not accepted the deal, which was double the initial offer, the High Court heard.
They are unlikely to pursue further action due to the high costs.
Lawyers had been expected to tell the court that the matter was over - with shareholders getting 82p-a-share, compared with the 200p-230p they paid.
However, Jonathan Nash QC, acting for the shareholders, said 13% have yet to make up their minds.
Further action unlikely
He added that he was hopeful a "significant" number would eventually accept the offer.
Just one investor with 2,000 shares said he was "dissatisfied", versus most of the 13% who claimed "they intend to accept the settlement proposal", the court heard.
The case had already been adjourned as the state-controlled bank and the claimants edged closer to a deal.
A group of "die hard" investors were reported to be keener on seeing Fred Goodwin and other executives from the bank's darkest days in 2008 in court, rather than settling.
There had been suggestions that these investors could continue to pursue the case, supposedly raising £7m to fund it.
However, Mr Nash told the court: "I wish to make it crystal clear the legal team has seen no evidence that funding is available."
Judge Robert Hildyard said the minority of rebel shareholders could apply for the trial to resume if they could prove they had sufficient funding by the end of July.
"In a difficult and novel situation, the process of bringing an end is not as easy as might be thought," Mr Hildyard told the court.
RBS said in a statement the decision was a "positive outcome".
The bank added: "87% of the remaining claimants by value have accepted the settlement offer and the trial has now been vacated. This includes the Action Group, which represents the individual retail claimants.
"The offer remains open for acceptance for a short period to the further 13%. It was made clear today in court that this delay is the result of procedural issues. None of the outstanding claimants have indicated any intention to continue the claim."
The case had been due to start on Monday, 22 May, and had been scheduled to last for 14 weeks.
However, it was adjourned and the parties began discussions over reaching a settlement.
The dispute centres on RBS's decision, during the financial crisis, to ask shareholders for billions of pounds worth of funds after it bought Dutch rival ABN Amro.
Shortly afterwards, the government was forced to prop up the bank with £45bn of taxpayers' money to save it from collapse. The state still owns a 72% stake in RBS.
The bank and former directors deny any wrongdoing.
The bank has already settled the majority of claims over the issue, but has not admitted liability.