The Paralympian athlete was jailed for five years in October for the culpable homicide of his girlfriend Reeva Steenkamp, whom he killed last year.
Prosecutors also want to challenge 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 Ms Steenkamp, a model and law graduate.
He 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 Masipa said she would rule on Wednesday whether the prosecution’s appeal could go ahead.
Pistorius was not in court on Tuesday when prosecutor Gerrie Nel outlined his case.
The prosecutor told Judge Masipa she had misinterpreted the law when she acquitted Pistorius of murder, and sentenced him to five years in prison.
“The precedent set by this court is shockingly low,” Mr Nel said.
However, 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,” defence 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.
It may seem like unnecessary legal wrangling but the state believes it has a strong case and wants the Supreme Court of Appeal to help deliver justice for Reeva Steenkamp.
The law makes provision for prosecutors to appeal on a matter of law but not on a factual finding.
If the state’s attempt fails, Pistorius could be eligible for parole and house arrest after serving 10 months. This is a prospect prosecutor Gerrie Nel is desperate to avoid.
He wants to undo what he has called a “grossly inappropriate” sentence and believes, if given the chance, a higher court would rule in his favour.
South African criminal lawyer Martin Hood told AFP news agency that he expected Judge Masipa to agree to the prosecution’s request because there was “just too much controversy about the judgement”.
“It doesn’t matter what the outcome of the appeal is. If the appeal is allowed then other judges will be able to comment on the decision, and that’s critical,” Mr Hood is quoted as saying.
In papers filed with the court in November, Mr Nel said the judge had “erred in over-emphasising the personal circumstances of the accused”.
“Not enough emphasis was placed on the horrendous manner in which the deceased died, coupled with the gruesome injuries she sustained when the accused shot and killed her,” he added.
The judge, Mr Nel said, had failed to sufficiently consider that 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.
Ms Steenkamp was shot dead at Pistorius’ home in Pretoria in the early hours of Valentine’s Day last year. He said he feared there was an intruder but he did not intend to kill.
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.