Pistorius's lawyers last month failed in their final legal bid to reverse a Supreme Court of Appeal (SCA) ruling that upgraded his conviction from culpable homicide -- the equivalent of manslaughter -- to murder.
The double-amputee killed Steenkamp, a model and law graduate, on Valentine's Day three years ago, saying he mistook her for an intruder when he shot four times through the door of his bedroom toilet.
"Your matter is postponed until June 13, and it will be heard until June 17, do you understand?" Judge Aubrey Ledwaba told Pistorius, who answered "Yes."
The former Paralympic champion, 29, faces a minimum 15-year jail term for murder, which may be reduced due to time he has already spent in prison.
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He was released from prison in October to live under house arrest at his uncle's property in Pretoria after serving one year of his five-year prison sentence for culpable homicide.
The SCA judges in December described his testimony at his trial in 2014 as "untruthful" and delivered a damning indictment of the original verdict.