Elish Angiolini QC, the Lord Advocate, is seeking a guideline from a five-judge appeal bench which would allow for “whole life” sentences and remove the sentencing discount of a third given in murder cases following a guilty plea.

The Crown believes that the system, established in part following the 2003 Du Plooy case, can result in excessive reductions in murder cases as opposed to other crimes.

In one of the cases it has brought before the court, murderer Robert Kelly had his punishment part of his life sentence reduced from 20 years to 15 years following his guilty plea.

Kelly, 34, strangled grandmother Agnes ‘Nessa’ Mechan, 64, and hid her body under floorboards.

The victim, a loan firm collector, disappeared in 2002 after calling at the home of Kelly, in the Govanhill area of Glasgow.

It was later discovered that he strangled her with a cord and robbed her of a handbag and 340 pounds in cash before dumping her corpse under floorboards and covering it with soil.

Her family went through more than four years of anguish and suffering before the body was finally found. Lord Brailsford, the judge who sentenced Kelly for the murder, described it as a cold-blooded and premeditated crime.

The move comes just weeks after Abdelbaset Ali Mohmed al Megrahi, the man convicted of the Lockerbie bombing, was freed early on compassionate grounds.

Kenny MacAskill, the Justice Secretary, decided to release Megrahi because he is dying of prostate cancer. His life sentence - a minimum term of 27 years - is one of the longest imposed by a Scottish court.

The Crown has taken the cases of three men convicted of murder to the Court of Criminal Appeal in Edinburgh claiming that the sentences they received were “unduly lenient”.

Anyone convicted of murder gets a sentence of life imprisonment, but the sentencing judge is obliged to fix a period - known as a “punishment part” - which must be served prior to the killer becoming eligible to apply for parole.

It was brought in following the adoption of the European Convention on Human Rights and informs the murderer of the minimum time he or she must serve in jail.

Ms Angiolini told the court that an appeal case in 2002 had led to an understanding that the range of punishment parts available to reflect the seriousness of the crime was “a relatively compressed scale from 12 years to 30 years”.

Former Royal Scots corporal Andrew Walker, who gunned down three people in an Army payroll robbery, had his minimum term reduced from 30 years to 27 years.

Mrs Angiolini said: As Lord Advocate I consider that is inadequate to reflect the wide range of conduct which may amount to murder and fails to reflect adequately the exceptionally serious cases of murder, particularly those involving multiple victims, terrorism or persistent sexual violence against vulnerable adults or children.

“I am asking the court to consider issuing a guideline opinion which will recognise that 30 years is not the absolute maximum punishment part and recognises explicitly that in some exceptional cases a punishment part which exceeds the natural life expectancy may be appropriate,” she said.

The Lord Advocate told the court that she was not seeking “a rigid tariff scheme” but wanted more detailed guidance for judges sentencing in murder cases.

She maintained it would enhance public confidence that judges were being consistent in their approach to dealing with murder cases.

In other jurisdictions, such as England, the worst cases of murder can attract “whole life” orders.

Mrs Angiolini said: “Despite a general decrease in crime, violent crime remains a persistent problem in too many communities in Scotland.”

She said the homicide rate per head of population in Scotland exceeded that of other parts of Britain, with 22 per million in 2007-08, compared with 14.6 in England and Wales and 14 in Northern Ireland.

The Lord Advocate said statistics indicated that just under half of the killings in Scotland were “committed by individuals using sharply pointed weapons”.

The head of the prosecution service said: “Knife crime in Scotland is a matter of profound concern.”

“I would ask Your Lordships to consider particular guidance to judges which reflects the court’s repugnance at the alacrity with which knives, and in particular swords, are carried in public in Scotland and used as weapons often against innocent strangers or passersby whose lives appear to be viewed by their assailants as a cheap commodity.”

The second murder case in which the Crown contends the punishment parts set were too lenient involves Brian Boyle, 21, and Greig Maddock, 22.

They were ordered to serve minimum terms of 15 years and 12 years respectively in 2007 after murdering father-of-two Brian Bowie in Dunfermline, Fife.

Mr Bowie, 35, was set on fire while still alive after being attacked and died in hospital five days later after sustaining full thickness burns to 32% of his body.

The victim was drinking at Boyle’s flat, but Boyle, who was aged 18 at the time, assaulted him, striking him on the head with a bottle and kicking and stamping on his head as he lay defenceless.

Mr Bowie was also stabbed in the leg before being dragged outside. Boyle’s friend, Maddock, arrived on the scene and lighter fuel was poured on the victim before he was set alight.

Two men, Raymond Anderson, 46, and James McDonald, 34, were given minimum terms of 35 years last year for the murder of Michael Lyons, 21, who was shot dead at a garage in Glasgow, but their cases have yet to come before the appeal court.

The Crown appeals in the Kelly and Boyle and Maddock cases are being heard by Scotland’s senior judge, the Lord Justice General, Lord Hamilton, sitting with Lord Reed, Lord Clark, Lord Mackay and Lady Dorrian. The judges are expected to give a decision at a later date.