Oscar Pistorius, 27, was jailed for five years in October for the culpable homicide of his girlfriend Reeva Steenkamp, whom he killed on Valentine’s Day 2013.
Prosecutors also want to challenge Oscar Pistorius’ acquittal on murder charges.
His lawyers opposed the appeal request and said the sentence was not lenient.
The double-amputee sprinter had been charged by the prosecution with the premeditated murder of Reeva Steenkamp, a model and law graduate.
Oscar Pistorius was also acquitted of the lesser murder charge of dolus eventualis by High Court Judge Thokozile Masipa.
In South African law, this charge – also known as common-law murder – applies if the accused knew they might kill someone but still went ahead with their course of action.
Judge Thokozile Masipa said she would rule on December 10 whether the prosecution’s appeal could go ahead.
Oscar Pistorius was not in court on December 9 when prosecutor Gerrie Nel outlined his case.
The prosecutor told Judge Masipa she had misinterpreted the law when she acquitted Oscar Pistorius of murder, and sentenced him to five years in prison.
“The precedent set by this court is shockingly low,” Gerrie Nel said.
However, Oscar Pistorius’ legal team argued that the prosecution’s case was flawed and the judge had correctly applied the law.
“It’s incorrect to say it’s a light sentence. It’s not,” defense lawyer Barry Roux said.
Addressing the judge, he added: “Their problem is they don’t like your factual finding. They don’t appreciate that. You absolutely, correctly applied the law.”
Correspondents say it is common in South Africa for the same judge to hear an appeal against their own verdicts.
Judges often grant the request because they are confident they applied the law correctly and their judgement will stand up to scrutiny.
South African criminal lawyer Martin Hood told AFP news agency that he expected Judge Thokozile Masipa to agree to the prosecution’s request because there was “just too much controversy about the judgement”.
In papers filed with the court in November, Gerrie Nel said the judge had “erred in over-emphasizing the personal circumstances of the accused”.
The judge, Gerrie Nel said, had failed to sufficiently consider that Oscar Pistorius had fired four shots “through a locked door into a small toilet cubicle from which there was no room to escape”.
The prosecution had called for the maximum 15-year sentence for culpable homicide, or manslaughter.
Oscar Pistorius is serving the sentence in the hospital wing of Pretoria’s Kgosi Mampuru II prison. He can apply to serve the rest of his sentence under house arrest after 10 months.
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