In a statement, they say claims Oscar Pistorius had received coaching for his emotional performance were “devoid of the truth”.
Oscar Pistorius, 27, has broken down on several occasions during the trial, often disrupting proceedings.
He denies intentionally killing Reeva Steenkamp in the early hours of Valentine’s Day last year.
Oscar Pistorius says he fired four shots through a locked toilet door out of fear, believing there was a burglar inside.
But the prosecution says the 29-year-old model and law graduate was deliberately killed after the couple had an argument.
South African columnist Jani Allan claimed Oscar Pistorius took acting lessons ahead of his trial in an open letter to the athlete last week, saying she had heard it “from a reliable source”.
“Oscar, you are the latest in a long line of faux heroes. Like so many who preceded you, you have betrayed your people and disappointed your fans,” Jani Allan wrote.
Oscar Pistorius’ family said they felt compelled to deny the claims after they were widely circulated in the media.
In a statement on the athlete’s website, spokeswoman Anneliese Burgess said Jani Allan had never met Oscar Pistorius and that any knowledge she had of him was “fictitious”.
“This type of comment makes a mockery of the enormous human tragedy involving the Steenkamp family and our client and his family,” it adds.
The allegations followed seven days of emotional testimony from Oscar Pistorius, who at times broke down in court and vomited when evidence from the post-mortem examination was presented to court.
Oscar Pistorius trial has been adjourned over the Easter period and will resume on May 5.
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