The 27-year-old returned to the High Court in Pretoria this week for a sentencing hearing after he was found guilty of culpable homicide (manslaughter).
Pistorius was convicted of killing his girlfriend Steenkamp by firing four gunshots through a toilet door at his home in the early hours of Valentine's Day last year.
Today, lawyer Dup de Bruyn released a statement on behalf of Steenkamp's parents, which read: "After Miss Steenkamp (the deceased) was killed the parents were in financial difficulties. We were contacted soon afterwards by Mr Pistorius's lawyers with an offer that Mr Pistorius would contribute an amount towards the parents' rental and living expenses.
"When the parents were made aware of this offer, they considered it carefully but decided, for various reasons, that they did not want any payment from Mr. Pistorius. This is also why we were instructed to advise that no civil claim would be instituted."
It was also claimed that Steenkamp's parents were "quite surprised" that Pistorius's lawyers had mentioned the payments after the athlete had asked his late girlfriend's family to keep the information confidential.