The National Prosecution Authority will present its case to a one-day hearing at the Supreme Court of Appeal in Bloemfontein. Judges are expected to hand down their ruling at a later date.
The Paralympic athlete shot dead Reeva Steenkamp in the early hours of Valentine's Day in 2013, when he fired four times through the door of his bedroom toilet -- an act, he says, that came from mistaking her for a burglar.
Pistorius was originally convicted of culpable homicide -- the equivalent of manslaughter -- in 2014, but the appeal court in Bloemfontein upgraded his conviction to murder in 2015.
Pistorius, 30, who is being held at the Atteridgeville Correctional Centre prison in Pretoria, will not be in court on Friday.
"We believe the sentence is shockingly low," NPA spokesman b told AFP.
"The court has discretion to deviate from the minimum sentence for murder of 15 years, after considering the circumstances, but we say that you cannot go so far below.
"We cannot allow a situation where we create a precedent for a person sentenced for murder. It is inappropriate if you look at the gravity of the offence."
Mfaku denied that the NPA was pursuing Pistorius due to his fame.
"It is not personal, we are addressing a principle here, we would have done this for anyone," he said.
'Pay for his crime'
A spokesman for the Pistorius family was not immediately available to comment, but his lawyers have previously said they accepted his current sentence.
At his sentencing last year, High Court judge Thokozile Masipa listed mitigating factors, including the athlete's claim he believed he was shooting an intruder.
"He cannot be at peace. I'm of the view that a long term of imprisonment will not serve justice," Masipa said.
But Steenkamp's father Barry told the court that he wanted Pistorius to "pay for his crime".
Members of the ruling African National Congress (ANC) women's league, who attended many court sessions, have criticised the sentence for failing to send a message against domestic violence in South Africa.
The year before he killed Steenkamp, Pistorius became the first double-amputee to race at the Olympics when he competed at the London 2012 games.
Previously a role model for disabled people worldwide, he was released from jail in 2015 after serving one year of a five-year term for culpable homicide.
He returned behind bars after his conviction for murder.
Pistorius, who pleaded not guilty at his trial in 2014, has always denied the accusation that he killed Steenkamp while in a rage.
He has insisted that he was trying to protect her.
In a television interview, he said he believed an intruder was in the house and "instant fear" drove him to grab his gun and walk on his stumps towards the bathroom.
"All of a sudden I hear a noise, at the toilet. I presumed it was the toilet door opening and before I knew it, I'd fired four shots," he said.
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