The Paralympic gold medalist admitted 29-year-old killing Reeva Steenkamp in February 2013 by firing four shots into the locked door of a toilet cubicle in what he said was the mistaken belief that an intruder was hiding behind it.
Pistorius, whose lower legs were amputated as a baby, is due to be released on Friday after serving 10 months of a five-year sentence, in line with South Africa's custodial guidelines for non-dangerous prisoners.
During sentencing, Judge Thokozile Masipa said the state had failed prove Pistorius' intent to kill when he fired.
Prosecutors want the verdict, equivalent to manslaughter, changed to murder because they argue that if Pistorius knew someone was behind the toilet door when he fired, he had the intention to kill, one of the prosecution team said.
"We filed the appeal today," National Prosecuting Authority spokesman Luvuyo Mfaku said.
Pistorius' legal team has a month to file its responseto the appeal, which the Supreme Court is expected to hear in November, Mfaku added.
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