June accuses the jailed athlete, 27, of only acting to try and “save his own skin” in court
June, 68, said she believed her daughter – who had only been dating Pistorius for less than three months – had “nagging doubts about their compatibility” and felt the relationship was coming to an end before she was shot dead on Valentine’s Day last year.
She said: “She had confided to me that she hadn’t slept with him.
“They’d shared a bed, but she was scared to take the relationship to that level. She wouldn’t want to sleep with Oscar if she wasn’t sure.
“I believe their relationship was coming to an end. In her heart of hearts, she didn’t think it was making either of them happy.”
June, who is due to release a book Reeva: a Mother’s Story, added that Pistorius is “gun-toting”, “trigger happy” , “possessive” and “shifty”.
She also added that she does not believe the athlete, who has been sentenced to five years in prison for the manslaughter of Reeva.
In an extract from her book in Times Magazine, she added: “It was Reeva’s bad luck that she met him, because sooner or later he would have killed someone. I do believe that.”
June also said she and Reeva’s father Barry, 71, have recurring nightmares about their daughter’s final moments and the fear she must have gone through.
“Both of us are haunted by the same nightmare. The vision of Reeva suffering this terrible trauma. Her terror and helplessness. Her yells for help piercing the silent night air,” added June.
“Barry agonises over what was going through her mind. ‘Where is anyone? Who is going to save me?’”
June added that she felt “unmoved” by Pistorius’ apology for shooting dead her daughter.
The Olympic sprinter was jailed for five years for killing his then-girlfriend, 29, but he could be out of prison in 10 months.
June describes Pistorius, 27, as a “pathetic figure”.
The extract focuses on the athlete’s public apology during the televised trial.
“It was an extraordinary moment. You could cut the atmosphere in the courtroom with a knife: silence, but for the sound of journalists tapping on their screens. It put me in an awkward position.
“Why decide to say sorry to me in a televised trial in front of the whole world? I was unmoved by his apology.
“I felt if I appeared to be sorry for him at this stage of his trial on the charge of premeditated murder, it would in the eyes of others lessen the awfulness of what he had done.”
“He was in the box trying to save his own skin after he had killed my daughter and I was sitting in that courtroom wanting to hear the factual truth, not to see emotions cloud the truth.”
Pistorius was also given a suspended three-year term for a firearms offence.
The sentence given to the amputee athlete has been criticised by some as too lenient, but Miss Steenkamp’s parents told ITV’s Good Morning Britain they accepted the sentence and “don’t want revenge”.
But they said their daughter’s death in the early hours of Valentine’s Day last year remained shrouded in mystery, and “only Oscar knows” the truth.
Pistorius, who the court heard has no income and no property after selling it during the trial, was driven away in a police van with barred windows after his sentencing on Tuesday.
He is expected to be held in the hospital section of a prison in Pretoria.
Mrs Steenkamp’s book is to be published on November 6.