In a major review of Scots criminal law carried out last year, judge Lord Carloway said the rule, which ensures all key evidence is backed by two sources, was "archaic" and no longer had a place in a modern legal system.
All other judges said they disagreed with the conclusion to abolish the current rule as they released their response today to a public consultation launched by the Scottish Government on the review.
The Senators of the College of Justice said corroboration, unique to Scotland, provided a "major safeguard" against miscarriages of justice.
Judges also said removing the rule would lead to "decreasing confidence in the legal system" and to lower rates of conviction generally.
They said: "In our view, it is often difficult to assess the true facts on the basis only of the evidence of one witness. A witness may be credible and plausible, yet not be telling the truth (or the whole truth).
"The Scottish courts have on many occasions been grateful for the requirement of corroboration, which in our view provides a major safeguard against miscarriages of justice."
They added: "One particularly anxious area is that of alleged sexual offences, where (without corroboration) the issue becomes one of the complainer's word against the accused's. Our concern is that the abolition of corroboration may result in miscarriages of justice."
Judges expressed concern about police procedure if the need for corroboration was removed.
"We are also concerned that the abolition of corroboration may result in less diligent police investigation pre-trial: knowing that corroboration is not required, there may be a relaxation in the search for supporting evidence (even though such may well exist)," they said.
"Furthermore the court or jury, faced with the dangers of one person's word against another's, may be reluctant to convict. In our experience, juries have always found corroborative evidence of great assistance.
"The current perception may be that the conviction rate in certain types of crime (for example, sexual offences) is low. It is our considered view that if corroboration were to be abolished, that would lead to decreasing confidence in the legal system, and to lower rates of conviction generally."
In 2010, Lord Carloway was asked to lead a review of Scots law and practice in the wake of a high-profile human rights decision by the UK Supreme Court. The Cadder ruling put an end to police being able to question suspects without the option of legal representation.
In his 400-page review, he wrote that the requirement for evidence to be corroborated has lain at the heart of the criminal justice system "since time immemorial" but was based on "medieval" thinking.
His 76 recommendations looked at four areas: custody, investigation, evidence and appeals.
Judges supported the majority of the Carloway Review proposals but stopped short of agreeing with the abolition of corroboration.
They also said that if the requirement is removed, additional changes should be made to the criminal justice system.
Consideration may have to be given to changing the current requirement for a verdict of guilty from a minimum of eight jury members out of 15 to the type of majority required in England, of 10 out of a jury of 12, they said.
Judges added: "In our view, if the requirement of corroboration were to be abolished, it would reinforce the case for retaining the 'not proven' verdict to allow a jury a principled third option where they found it impossible to work out which of the complainer or the accused was telling the truth."
The consultation seeking views on reforms of the legal system closed on October 5.
A Scottish Government spokeswoman said: "The proposed abolition of the requirement for corroboration was recommended in an independent review by Lord Carloway. Lord Carloway's recommendations have been subject to a Government consultation exercise.
"The consultation specifically sought views on whether any additional safeguards would be required as a result of removing the corroboration rule and we will carefully consider all responses."
Earlier this year, Lord Carloway was appointed the country's second top judge when he took up the role of Lord Justice Clerk.
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