The double-amputee killed Reeva Steenkamp, a model and law graduate, in the early hours of Valentine’s Day in 2013, saying he mistook her for an intruder when he fired four times through the door of his bedroom toilet.
Pistorius tried to greet Steenkamp’s relatives as he entered the court on Tuesday but they did not respond.
“He has developed a serious psychiatric condition which has become worse in the past two years,” psychologist Jonathan Scholtz, called by the defence, told the court on Monday.
“Further imprisonment would have a detrimental effect on him.”
Scholtz said that during recent interviews Pistorius had displayed signs of “post-traumatic stress disorder, anxiety disorder and depressive disorder”.
In March, Pistorius’s lawyers failed in their legal bid to reverse a Supreme Court of Appeal judgement that upgraded his original conviction from culpable homicide — the equivalent of manslaughter — to murder.
The original trial judge Thokozile Masipa is expected to pass a new sentence after hearing arguments from both prosecution and defence.
Pistorius faces a minimum 15-year jail term for murder, but his sentence could be reduced due to time already spent in prison and mitigating factors, including his disability.
Steenkamp’s parents were both in court, and her father Barry may take the witness stand to ask the court to impose a lengthy punishment.
If he does, it will be the first time that one of Steenkamp’s parents has testified in the case.
Pistorius has shunned the media during years of intense coverage since Steenkamp’s killing, but his family have revealed that he has given his first interview, due to air on British broadcaster ITV later this month.
The interview drew a sharp attack on Monday from state prosecutor Gerrie Nel, who said it proved that Pistorius was capable of testifying.
“He would rather give his version to the TV than to court,” said Nel, who accused psychologist Scholtz of being biased.
Pistorius was released from jail last October to live under house arrest at his uncle’s mansion in Pretoria after serving one year of his five-year sentence for culpable homicide.
Since being convicted of murder, Pistorius has been on bail and allowed to leave his uncle’s house at set times, but not travel further than 20 kilometres (12 miles) without permission.
The hearing — held in the same courtroom as the original trial — is scheduled to last one week.
Pistorius has always denied killing Steenkamp in a rage and, during his dramatic seven-month trial in 2014, sobbed in the dock as details of his lover’s death were examined in excruciating detail.
The year before he killed Steenkamp, Pistorius became the first double-amputee to race at Olympic level when he appeared at the London 2012 games.