The Paralympian was released from prison last month after serving one year of his five-year term for killing his girlfriend Reeva Steenkamp.
Pistorius, 28, shot her through a locked bathroom door in 2013 but insists he thought she was an intruder.
He could be sent back to jail if appeal judges overturn the original verdict.
Pistorius is currently under house arrest, and did not attend the hearing at South Africa's Supreme Court of Appeal in Bloemfontein.
The proceedings were broadcast live on television.
State prosecutor Gerrie Nel outlined the state's case for the verdict to be changed to murder from culpable homicide, or manslaughter.
The five appeal court judges did not consider the facts but the application of the law, in a highly technical case.
The prosecution said that Judge Thokozile Masipa incorrectly applied the law of murder. It argued that Pistorius should have foreseen the result of his actions, namely that shooting four times into a closed toilet cubicle door would result in a person's death.
The athlete said he believed there was an intruder in the house and thought his girlfriend was in the bedroom.
The prosecution argued that who was behind the bathroom door was irrelevant, and Pistorius's intent was to kill.
The prosecution also want his jail sentence to be increased from five years to a minimum of 15 years.
The final ruling will not be known for some weeks, reports say.
Pistorius was found guilty of the culpable homicide of his 29-year-old girlfriend at a trial in October last year.
Ms Steenkamp's relatives have said they think Pistorius is "getting off lightly".
The double amputee was released from prison on 19 October. Under South African law, he was eligible for release under "correctional supervision", having served a sixth of his sentence.
His family said he would "strictly" adhere to his parole conditions at his uncle's upmarket home in Pretoria.
Pistorius competed in the 400m at the London 2012 Olympics, wearing carbon-fibre blades to run against able-bodied athletes.
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5 years, 11 months ago
Cape Town Uber driver Eric Selaelo was taken aback by the news. Like many South Africans, he was expecting double amputee and Olympic sprinter Oscar Pistorius to get at least 10 years for the murder of his girlfriend Reeva Steenkamp in a case that has riveted the country’s attention for most of the past three years.
6 years, 8 months ago