In a statement released on Monday, June and Barry Steenkamp said this was a very sad and traumatic time for them but they understood the intense media interest, Eyewitness News reported on Tuesday.
The Steenkamps requested the media to respect their privacy and said they would not be doing any interviews for the time being.
According to the report, Attorney Mike Venter and senior advocate Dup de Bruyn were appointed by the Steenkamp family to look after their interests.
Pistorius was charged with murder after Steenkamp was shot and killed at his home in Pretoria on February 14 and was granted bail of R1-million on Friday. He was allowed to pay an initial instalment of R100 000, with the balance due by March 1.
Steenkamp was cremated in a private ceremony in Port Elizabeth on February 19.
In an affidavit submitted as part of his application for bail, Pistorius said he thought there was an intruder in his house when he fired the shots.
Leaked CCTV footage
Meanwhile closed-circuit television footage of Steenkamp aired on Carte Blanche, the Star reported on Tuesday.
The leaked footage, which was aired on Sunday night, shows Steenkamp arriving at Silver Woods Country Estate in Pretoria hours before she was killed.
The recording was made at the vehicle entrance to the estate.
According to the newspaper report, Steenkamp was seen pulling up to the checkpoint in a dark-grey Mini Cooper.
She appeared to be exchanging a joke with another guard. As she drives away, the guard waves and laughs.
CCTV footage taken 10 minutes later shows a white BMW allegedly with Pistorius inside, arriving at the estate.
Pistorius's next court appearance is on June 4. – Sapa