Chief prosecutor Gerrie Nel has revealed in Court that Oscar Pistorius is making a monthly payment of 6,000 rand to Ms Steenkamp’s parents after they asked for help.
Mr Nel added that those payments would be returned in full.
There was also a separate offer of 375,000 South African rand to the family of girlfriend Reeva Steenkamp after he killed her, but they rejected it because they did not want “blood money”.
The revelations emerged while Mr Nel was cross-examining a social worker over what Pistorius’ punishment should be for shooting his girlfriend on Valentine’s Day 2013.
Outside the courtroom, a lawyer for Ms Steenkamp’s parents said they had asked him to contact Pistorius’ legal team weeks after the shooting because they were struggling financially.
Pistorius offered them monthly payments and asked for them to be kept confidential, the Steenkamps’ lawyer Dup de Bruyn said.
Ms Steenkamp’s mother June referred to the other offer of 375,000 rand that the family rejected as “blood money”, and asked prosecutor Mr Nel to call it that in court, Mr de Bruyn said.
“The words ‘blood money’ are her words,” the lawyer added.
Judge Thokozile Masipa found Pistorius, 27, not guilty of murder last month. She concluded he had acted hastily and with excessive force, but did not intend to kill Ms Steenkamp, a 29-year-old model.
The judge has wide latitude when deciding on a sentence. Pistorius could receive a fine and a suspended jail term or up to 15 years in prison.
Ms Vergeer and another social worker recommended that Pistorius be given a three-year correctional supervision sentence, which would place him under house arrest for periods and require him to carry out community service.
Prosecutors insist that such a sentence would be inappropriate and say Pistorius should be sent to prison, citing the level of negligence he showed when he fired his 9mm pistol without checking who was behind the door.
Family members of Pistorius and Ms Steenkamp attended the second day of the trial’s sentencing hearing, which is expected to last for a week or so.