However, Reeva Steenkamp’s family rejected the sum as “blood money”, prosecutor Gerrie Nel revealed during his sentencing hearing.
Earlier, a defense witness told the court that Oscar Pistorius, 27, would be physically at risk if sent to prison.
The Paralympic champion has been found guilty of culpable homicide, but cleared of murder.
The defense is trying to show that prison would be an inappropriate punishment.
Oscar Pistorius’ offer of a lump sum of 375,000 rand to the Steenkamp family emerged on the second day of his sentencing hearing, during the cross-examination of defense witness Annette Vergeer.
Gerrie Nel told Annette Vergeer that Oscar Pistorius raised the funds from selling his car.
The prosecutor added that Reeva Steenkamp’s mother, June, had rejected the offer.
“She does not want blood money,” he said.
Gerrie Nel also highlighted separate monthly payments of 6,000 rand ($540) made by Oscar Pistorius to the Steenkamps – who were short of money after their daughter’s death.
The prosecutor said these funds – mentioned in Annette Vergeer’s report – would be “paid back to the accused in full – every cent”.
The Steenkamps’ lawyer, Dup De Bruyn, explained that the couple were now “reasonably comfortable” after he had negotiated a series of media deals concerning their daughter’s death.
The Pistorius family later accused Gerrie Nel of giving a distorted picture in court of the financial agreement with the Steenkamps, and said they would provide a full statement on Wednesday, October 15.
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