Slain model Reeva Steenkamp "can now rest in peace", say her family after a South African court doubled Oscar Pistorious' jail term for her murder.

The disgraced former Paralympian's sentence has been increased from six years to 13 years and five months.

The court yesterday upheld an appeal by prosecutors, who challenged Pistorius' original six-year jail sentence saying it was too lenient and "inappropriate" for his conviction of murder in the shooting of girlfriend Reeva Steenkamp in 2013.

The decision was "justice for Reeva," a family spokeswoman said. They hope "this is the end of the road and that everyone can move forward."

But Pistorius' brother, Carl, simply Tweeted he was 'Shattered. Heartbroken. Gutted. I am flabbergasted!"

Supreme Court Justice Willie Seriti said he believed Pistorius had failed to explain why he opened fire and "does not appreciate the gravity of his actions".

"I find it difficult on the evidence to accept that the respondent is genuinely remorseful," Seriti wrote in a document detailing his decision.

The Blade Runner, who turned 31 on Wednesday, was initially convicted of manslaughter but also had that conviction overturned and replaced with a murder conviction by the Supreme Court.

The minimum sentence for murder in South Africa is 15 years.

The prosecution argued that Pistorius' disability should not have been a mitigating factor and that the athlete, who wept regularly throughout the trial, had not shown genuine remorse, but rather felt sorry for himself and regretted his actions.

The double-amputee sprinter maintains he believed Steenkamp was an intruder when he shot her through the bathroom door on Valentine's Day, 2013.

It was the second time the prosecution had appealed.

Pistorius was originally found guilty of culpable homicide, but this was changed to murder on appeal.

Pistorius, whose lower legs were amputated because of a congenital defect, soared to international fame after becoming the first amputee to compete in the 2012 Olympic Games.