Pistorius has spent 10 months in jail for shooting dead his girlfriend Reeva Steenkamp, after his conviction for manslaughter last year.
The Olympic athlete insists he mistook Ms Steenkamp for an intruder.
State prosecutors want his conviction to be reviewed and converted to murder, with a minimum sentence of 15 years.
Pistorius was jailed for five years in 2014 for the culpable homicide of Reeva Steenkamp, a charge equivalent to manslaughte.
Under South African law, Pistorius is eligible for release under "correctional supervision", having served a sixth of his sentence.
After being freed, he would serve the rest of his term under house arrest.
During sentencing, Judge Thokozile Masipa said the state had failed to prove Pistorius' intent to kill when he fired.
His defence team now has a month to file its response.
Ms Steenkamp's parents have said that the time he has served is "not enough for taking a life".
The double amputee shot and killed Ms Steenkamp through a locked bathroom door at his Pretoria home, believing she was an intruder, he told his trial.
In March a Johannesburg court blocked his legal team's attempts to stop the prosecutors' appeal.
Pistorius' girlfriend Reeva Steenkamp was a lawyer, model and TV star
Pistorius was born without the fibulas in both of his legs, and had surgery to amputate both below the knee while still a baby.
He went on to become one of South Africa's best-known sports stars, and was the first amputee to compete against able-bodied athletes, at the 2012 London Olympics.
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