The Paralympic gold medallist was sentenced in July for murdering his girlfriend, Reeva Steenkamp, in 2013. At the time, some legal experts described the prison term as lenient.
"The sentence of six years imprisonment, in all the circumstances, is disproportionate to the crime of murder committed, that is to say, shockingly too lenient," the National Prosecuting Authority (NPA) said.
"(The sentence) resulted in an injustice and has the potential to bring the administration of justice into disrepute."
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The jail term was less than half the 15-years sought by prosecutors, who said Pistorius had shown no remorse for the 2013 shooting. The appeal papers will be filed on Thursday.
A Pistorius family spokeswoman could not be immediately reached for comment.
(Reporting by Zandi Shabalala; Editing by Joe Brock)
