JOHANNESBURG (AFP) -- A South African judge on Friday rejected the state's appeal seeking a longer jail sentence for Paralympian Oscar Pistorius, who is serving a six-year term for killing his girlfriend three years ago.

Thokozile Masipa -- the same judge who imposed the sentence last month -- said in the High Court in Johannesburg that she was not persuaded there was a "reasonable prospect of success on appeal".

"The application for leave to appeal against the sentence is dismissed with costs," she said.

The prosecution had been pushing for a longer sentence against the fallen 29-year-old sprint star over the 2013 murder of Reeva Steenkamp.

"The sentence of six years is shockingly lenient and disturbingly inappropriate," prosecutor Gerrie Nel argued in court.

Pistorius shot Steenkamp, a model and law graduate, in the early hours of Valentine's Day in 2013, saying he mistook her for a burglar when he fired four times through the door of his bedroom toilet.

At his sentencing in July, Masipa listed mitigating factors for ordering Pistorius to serve less than half the minimum 15-year term for murder, including the athlete's claim he believed he was shooting an intruder.

"I'm of the view that a long term of imprisonment will not serve justice,"

Masipa said then.

But Nel argued that the six-year sentence was flawed and that it should be appealed.

"Another court may find that this court misdirected itself," said Nel.

Masipa was also the judge who had originally convicted Pistorius of the lesser charge of culpable homicide, the equivalent of manslaughter, in 2014.

An appeals court upgraded his conviction to murder in December last year.

Pistorius's defence said it was an "insult" to suggest that the court's sentencing had been flawed and that it was time the case came to a close.

"Enough is enough. What does the state want?" defence lawyer Barry Roux said.

"This process has been exhausted beyond the point of exhaustion," he added, accusing the prosecution of sending Pistorius "like a ping pong ball between courts".

Pistorius, who pleaded not guilty at his high-profile trial, has always denied killing 29-year-old Steenkamp in a rage, saying he was trying to protect her.

South African media reports earlier this month said that Pistorius had been put on suicide watch following mysterious wrist injuries.

The year before he killed Steenkamp, Pistorius -- known as the Blade Runner -- became the first double-amputee to race at Olympic level when he appeared at the London 2012 Games.