Judgement has been reserved in an appeal over whether athlete Oscar Pistorius should be convicted of murder instead of culpable homicide.

A hearing started this morning after prosecutors lodged an appeal.

The athlete is currently under house arrest after serving less than a year in prison for killing his girlfriend.

He killed Reeva Steenkamp after firing a gun through his bathroom door, claiming he mistook her for an intruder.

The runner is currently under house arrest at his uncle's luxurious home in Pretoria after serving less than a year in prison for killing his girlfriend on Valentine's Day 2013.

Under South African law, the athlete became eligible to be put under house arrest after serving a sixth of that sentence.

He was released from jail a fortnight ago and is serving his house arrest at his uncle Arnold's spacious mansion complete with swimming pool, private gym and separate cottage.

Reeva's mother, June Steenkamp, has travelled to Bloemfontein to support South African State prosecutors who are trying to convince an appeal court panel that the judge at the runner's trial last year reached the wrong verdict.

She told Newstalk last week Pistorius may have gotten a longer sentence if it was not for his fame.

The state prosecutors want the appeal court panel of five judges to set aside the original conviction of culpable homicide - known as manslaughter in other countries.

A murder conviction carries a much heftier sentence: a minimum of 15 years in jail in South Africa.

The state claim the trial judge misinterpreted the law of dolus eventualis - a Latin legal phrase meaning the act was carried out by the accused knowing it would lead to death and the accused went through with it anyway.

The prosecutors say the judge wrongly applied the strict questions of law, and then answered them wrongly.

In the 45 pages which form the main basis of the state's appeal argument, the prosecutors list over and over what they see as the judge's mistakes: they quote her from her judgement saying, "The question is: did the accused foresee the possibility of the resultant death, yet persisted in the deed reckless whether death ensued or not? In the circumstances of this case the answer has to be no".

The prosecutors insist this is wrong.

They point out that the runner was an expert marksman who would have certainly known that by shooting into a confined space like the toilet cubicle, it would definitely lead to the death of whoever was behind the door.

The panel can order a retrial; it can dismiss the appeal or it can overturn the original verdict and impose the more serious murder one as well as change the sentence.

The runner himself was not expected to be in court to watch his lawyers do battle for him again.

But the judge has now adjourned the case.