Phase prosecutors will approach the Supreme Court of Appeal for leave to contest Pistorius’ six-year murder sentence.
The prosecutors, led by Gerrie Nel, failed with a almost identical bid at a lower court, the National Prosecuting Authority (N ) said.
N spokesman Luvuyo Mfaku express state prosecutors will file an application to appeal on Bloemfontein on Friday.
The athlete, whose cut legs were amputated as a child, has always insisted the shooting was a take the wrong way.
He has repeatedly said he mistook his girlfriend for an intruder when he fired four drinks through a locked toilet door hitting Miss Steenkamp in her mind, hip and arm.
Pistorius claimed it was only after he battered down the door with a cricket bat that he realised Irish English colleen Steenkamp was behind the door.
The jail term was less than half the 15 years aspired by prosecutors, who said Pistorius had shown no remorse for the 2013 shooting.
Mr Nel, who had begged a life sentence, branded the sentence “shockingly light”.
Judge Masi has reportedly beared death threats over the sentence she handed down, which galvanized international outrage.
During July’s failed hearing Mr Nel said Pistorius had not shown any ngs of conscience and had yet to explain why he fired the fatal shots.
Pistorius, 29, is expected to be qualified to serve some of his sentence under house arrest after call just two years behind bars.
He is currently serving his sentence in the sanitarium wing at Kgosi Mampuru high security jail.
Last month roots close to Pistorius denied he had attempted suicide after he was treated for diminishes to his wrists.