Oscar Pistorius will remain under house arrest pending his sentencing for his murder conviction, after a South African judge granted bail to the Olympic athlete.

The country's Supreme Court of Appeal convicted Pistorius last Thursday of murdering girlfriend Reeva Steenkamp in 2013, overturning a lower court's conviction of the lesser crime of manslaughter. The appeals court then said the double-amputee Olympian should be sentenced by the lower court.

Judge Aubrey Ledwaba of that court, the North Gauteng High Court in Pretoria, granted Pistorius bail of $692 and extended his house arrest until his sentencing hearing, which he set for April 18 2016.

The judge said Pistorius will be placed under electronic monitoring and may only leave his uncle's home between 7am and 12pm.

Pistorius may not travel further than a 20km radius outside of his uncle's mansion in a Pretoria suburb, the judge ruled. He must also hand over his passport to the police.

Earlier, the state argued that Pistorius may try to flee, and asked for strict bail conditions.

"We have a convicted murderer applying for bail so the conditions should be stricter," said prosecutor Gerrie Nel.

Pistorius's bail is a fraction of the $113,000 bail he paid when he first appeared in court over the 2013 shooting.

In the meantime, Pistorius's legal team plan to appeal against his murder conviction in South Africa's highest court, the Constitutional Court, chief defence lawyer Barry Roux said.

The former track star's lawyer did not say on what basis he would be appealing.

Prosecutor Mr Nel told the court that he doubted that this next appeal would be successful.

"We're not convinced that the accused has made out a good case and that his application to the Constitutional Court will be successful, but we acknowledge that he has the right to bring such an application," he said.

Pistorius shot Miss Steenkamp through the door of a toilet cubicle in his home in the early hours of Valentine's Day 2013. Prosecutors said he killed her after an argument; Pistorius said he killed her by mistake, thinking there was an intruder in the house.

The appeals court said that, regardless of who was behind the door, Pistorius should have known someone could be killed if he fired multiple times. Under South African law, a person can be convicted of murder if he or she foresaw the possibility of someone dying through their actions and went ahead anyway.

Pistorius was placed under house arrest in October after serving one year of a five-year prison sentence for the earlier manslaughter conviction.

During Tuesday's court appearance, the first time he has appeared in court in more than a year, Pistorius was dressed in a dark suit. His demeanor was calm and he spoke softly with his lawyer and others before proceedings began. He even grinned.

A champion athlete, before the killing of Miss Steenkamp, Pistorius had been televised at sporting events and seen in magazines in advertisements.

In contrast, he has rarely been seen in public while under house arrest.

Last weekend, a South African newspaper published a photograph of Pistorius sitting in a car. On November 14, video filmed on a mobile phone emerged of Pistorius reporting to a Pretoria police station as part of his community service. On his 29th birthday last month, a relative tweeted a photograph of a smiling Pistorius surrounded by children.

Pistorius travelled to North Gauteng High Court from his uncle's mansion in Pretoria, where he had been serving his house arrest for the manslaughter conviction. He will now remain there under house arrest until sentencing.

The minimum sentence for murder in South Africa is 15 years, though a judge can reduce that sentence for what the law describes as exceptional circumstances.