South African judges have heard an appeal on whether athlete Oscar Pistorius should be convicted of murder instead of culpable homicide.

The Paralympian was transferred to house arrest last month after serving one year of his five-year term for killing his girlfriend Reeva Steenkamp.

Pistorius, 28, shot her through a locked toilet door in 2013 but insists he thought she was an intruder.

No date was set for the judgement that could see Pistorius return to prison.

Pistorius and his family did not attend the hearing at South Africa's Supreme Court of Appeal in Bloemfontein.

Ms Steenkamp's mother, June, was present, as well as some women activists of the governing African National Congress who said they came to show solidarity with her.

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.

What is on everybody's lips is what Pistorius' lawyer Barry Roux was overheard saying at the end of the hearing. "I'm going to lose", he is reported to have said in a conversation with Mr Nel while their microphones were still open.

But the context in which he made the comment is unclear so it would be wrong to conclude that he conceded victory to his rival.

What is clear, though, is that Mr Roux had a tougher time in court, and there are many here who feel that the scales of justice tilted in favour of a murder conviction. But this case has thrown up so many twists and turns that no-one can confidently predict which way the court will rule.

The five judges who heard the appeal are among the most senior in South Africa, and came from across the racial and gender divide. It will, therefore, be difficult to fault their judgement. They did not take new evidence, but heard arguments from both sides on whether the trial judge interpreted the law correctly, especially the charge of dolus eventualis, also known as common-law murder.

In South African law, this charge applies if the accused knew they might kill someone but still went ahead with their course of action. The prosecution argued that Pistorius should have foreseen that by firing four shots through a locked door into a toilet cubicle, the person behind the door would have been killed.

Trial judge Thokozile Masipa disagreed, and Mr Roux did his best to convince the appeal judges to uphold her verdict. Was it enough to keep Pistorius out of jail?

Mr Roux told the judges that the athlete suffered from an anxiety disorder, and he fired in quick succession.

"The law is not designed to punish you for a wrong state of mind," he added.

Pistorius' action was lawful, and he genuinely believed that he was shooting at an intruder, Mr Roux said.

During his trial, 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 toilet door was irrelevant, and Pistorius' 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.