Oliveira, who beat Pistorius in the 200 meters at the Paralympics in London last year, and Pistorius were to run a straight 200 on Copacabana beach in Rio de Janeiro on March 31.
Pistorius was charged with the murder of Steenkamp after she was shot dead at the home of the multiple Paralympic champion on Thursday. South African prosecutors have said they will pursue a more serious premeditated murder charge against the 26-year-old Pistorius, leaving him possibly facing a life sentence.
"I can't plan anything," Van Zyl said of Pistorius' immediate running career, which was not a priority after the murder charge and Steenkamp's death.
"I will only have him run when he is in a condition to run as a world-class athlete. Physically and mentally fit."Meanwhile, he also states that Pistorius has received "overwhelming support" from his fans.
Peet van Zyl said outside the Brooklyn police station that "international fans from literally all over the world" have sent their good wishes to Pistorius.
Funeral on TuesdayJohannesburg: The family of Reeva Steenkamp says her body is back in her hometown of Port Elizabeth and a private funeral has been planned for Tuesday. Adam Steenkamp, the late model and law graduate’s brother, says “Reeva is back home”.
Steenkamp will be cremated in a ceremony closed to the public and the media in the city.