Granting anonymity would undermine our system of open justice and raise difficult questions on where to draw any line

Scottish Executive spokesman

The movement also wanted a new crime of false rape allegation and the creation of a false rape accuser register "similar to the register of sexual offenders".

But MSPs Phil Gallie and Gordon Jackson who sit on the justice committee said they had some sympathy with the suggestion, but other members felt accusations of rape should be dealt with in the same way as other charges.

Labour MSP and QC Gordon Jackson said it could lead the courts open to the charge of double-standards.

However, Mr Wallace said it was important to protect the anonymity of the victim or women may be deterred from coming forward to give evidence in rape trials.

He said there was no evidence of a widespread practice of false accusation. And there were safeguards for the accused before being brought to trial.

Mr Wallace added that rape trials were not undertaken lightly. And, as in any other case, it was important that the name of the accused should be known.

Earlier, a spokesman for the Scottish Executive said: "We understand the concerns for those who are falsely accused of rape but we are not convinced that it is a widespread problem justifying legislation.

"Granting anonymity would undermine our system of open justice and raise difficult questions on where to draw any line.

"There is a clear distinction between a victim of rape and the accused in the eyes of the criminal justice system and it's the accused that's on trial and not the victim."

The committee took evidence on the issues from a number of organisations in March.

Jim Wallace rejected the call for anonymity

And the Scottish Human Rights Centre, Victim Support Scotland and the Law Society of Scotland indicated some sympathy for the idea of anonymity.

They argued the victim and the accused were often known to each other and the protection of anonymity could benefit both parties.

But Scottish Women's Aid and the Rape Crisis Centre did not back a change in the law.

Rather, they argued that the accused in a rape trial should not expect any preferential treatment over the accused of any other serious crime.