Oscar Pistorius, 28, was released from prison last month after serving one year of his five-year term for killing his girlfriend Reeva Steenkamp.
The Paralympic champion shot Reeva Steenkamp through a locked bathroom door in 2013 but insists he thought she was an intruder.
Oscar Pistorius could be sent back to jail if appeal judges overturn the original verdict.
He is currently under house arrest, and is not attending the hearing at South Africa’s Supreme Court of Appeal in Bloemfontein.
The proceedings are being broadcast live on TV.
State prosecutor Gerrie Nel has been outlining the state’s case for the verdict to be changed to murder from culpable homicide, or manslaughter.
The prosecution says that Judge Thokozile Masipa incorrectly applied the law of murder. It argues that Oscar Pistorius should have foreseen the result of his actions, namely that shooting four times through a closed bathroom door would result in a person’s death.
Oscar Pistorius said he believed there was an intruder in the house and thought Reeva Steenkamp was in the bedroom.
The prosecution will argue that who was behind the bathroom door is irrelevant, and Oscar Pistorius’ intent was to kill.
The final ruling will not be known for some weeks, reports say.
Oscar Pistorius was found guilty of the culpable homicide of his 29-year-old girlfriend at a trial in October 2014.
Reeva Steenkamp’s relatives have said they think Oscar Pistorius is “getting off lightly”.
The double amputee was released from prison on October 19. Under South African law, Oscar Pistorius was eligible for release under “correctional supervision”, having served a sixth of his sentence.
Oscar Pistorius’ family said he would “strictly” adhere to his parole conditions at his uncle’s upmarket home in Pretoria.
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