The adjournment, which was agreed by the claimants and the defendants, was granted at a brief hearing in London by Mr Justice Hildyard.
He was told by Jonathan Nash QC, for the shareholders: “The parties are currently involved in settlement discussions and are hopeful of making progress.”
Mr Nash added: “They have agreed that these discussions would be facilitated by allowing a further period of time for them to continue before the trial begins.
“On that basis they have also agreed that the start of the trial should be deferred by 24 hours until 10.30 tomorrow.”
David Railton QC, for the defendants, said “that is agreed”.
The judge gave the go-ahead for the adjournment on the basis that the parties agreed there should be a delay for talks and the assurance given that there was a prospect that the “matter can be brought to a conclusion”.
He added: “Obviously I would wish to facilitate that result.”
Chief executive Ross McEwan is said to have told the bank’s lawyers on Sunday to offer 82p a share, although it remains unclear whether it would be accepted by investors, a report by Sky News said.
It is understood that the judge could now adjourn the start of the trial by one day to allow settlement talks to continue.
Former boss Fred Goodwin is expected to defend his role in the lender’s near-collapse at the height of the financial crisis during a 14-week trial at London’s High Court.
Mr Goodwin and a raft of former executives are on course for a public grilling as part of a £700 million lawsuit brought against the lender by 9,000 retail investors and 18 institutions in the RBS Shareholder Action Group.
The majority of the claims have been settled out of court.
Disgraced former chief executive Mr Goodwin - who was stripped of his knighthood following the bank’s near-collapse - will answer questions over the events leading up to the Government’s £45.5 billion bailout nine years ago.
The legal action centres on a rights issue overseen by Mr Goodwin in April 2008 when RBS asked existing shareholders to pump £12 billion into the bank after leading a consortium that spent £49 billion on Dutch lender ABN Amro.
Shareholders claim they were left nursing hefty losses following the cash call after RBS shares plunged 90% and the Government was forced to step in when the deal turned toxic.