A prosecution application to appeal against the manslaughter conviction and five-year prison sentence given to Oscar Pistorius will be heard in a South African court on December 9.
Prosecutors say Pistorius should have been found guilty of murder for killing girlfriend Reeva Steenkamp.
The appeal against Judge Thokozile Masipa's initial verdict and sentence has "reasonable prospects" of success, they said.
Judge Masipa found the double-amputee Olympic runner not guilty of murder for shooting Ms Steenkamp through a toilet cubicle door in his home, ruling that he did not intend to kill when he fired four times.
Pistorius was instead convicted of culpable homicide, or manslaughter, because the judge said he acted negligently.
The athlete testified that he mistook Ms Steenkamp for an intruder in his home when he killed her in the pre-dawn hours of February 14 last year.
His five-year sentence means he could be released after serving 10 months in jail to complete the sentence under house arrest at his uncle's luxurious Pretoria home.
South Africa's National Prosecuting Authority (NPA) said it had been informed by defence lawyers for Pistorius that they would oppose the appeal.
If he is found guilty of murder on the appeal, he would face a minimum of 15 years in prison.
Prosecutors must first apply to Judge Masipa for permission to ultimately appeal her decisions in the Supreme Court of Appeal.
Their initial application will be heard next month by Judge Masipa at North Gauteng High Court, the Pretoria courthouse where Pistorius' seven-month murder trial was held.
The prosecution believes the judge may have made an error by ruling Pistorius intended to shoot into the small toilet cubicle but did not intend to kill anyone.
Prosecutors have cited a section of South African law called dolus eventualis, which says someone should be found guilty of murder if they foresaw the possibility of a person dying through their actions and went ahead - as they argued Pistorius did.
"The NPA reiterates that the decision to appeal was taken on the basis that it believes there exists reasonable prospects of a successful appeal based on a question of law," the state prosecuting body said.
The NPA wants "clarity" from the Supreme Court of Appeal over the principle of dolus eventualis, it said.
It has not yet been decided if the Olympic runner, who is in jail in the same city, will attend the hearing, his lawyer said.
He is entitled to be there and can apply to be released from prison on bail if the appeal goes ahead, prosecution spokesman Nathi Mncube said.
Pistorius' lawyer, Brian Webber, said he had not discussed those possibilities with his client.
The runner, who turns 28 this month, is in Kgosi Mampuru II prison, where he has been temporarily moved to a new cell because of a flood started by another inmate who was arguing with guards, City Press newspaper said.
Pistorius' defence team "would be very nervous" if the case was referred to the Supreme Court of Appeal, legal expert Marius du Toit said, because of the chance of a murder conviction.