"Oscar is not back on any official training programme," read the statement from his family. "This may change in future, but this will be a decision taken by Oscar."
The South African, who competed at both the Olympics and Paralympics in London last year, could return to competitive action after a court
changed his bail restrictions
to allow him to travel abroad for events.
He denies murdering the 29-year-old Steenkamp, who was
shot and killed
at his Pretoria home on 14 February.
The family statement continued: "At this point, Oscar is still in an extremely traumatised state and has made it clear to all of us that he is not able or willing to even contemplate this issue at this stage.
"Against this backdrop, we can confirm that we did have a meeting with Oscar yesterday [Wednesday] where various family members and his trainer were present. We all encouraged him to get back onto the track to help stabilise him emotionally.
Pistorius - the athlete
• Pistorius had his lower legs amputated at the age of 11 months, having been born without a fibula in either leg
• His parents, Henke and Sheila, were advised that having the amputation done before he had learnt to walk would be less traumatic
• By the age of two, Pistorius had his first pair of prosthetic legs
• He played water polo and rugby in secondary school. He also played cricket, tennis, took part in triathlons and Olympic club wrestling and was an enthusiastic boxer
• In June 2003, he shattered his knee playing rugby and on the advice of doctors took up track running to aid his rehabilitation
• Pistorius has won six Paralympic gold medals
"Oscar has been out running on a number of isolated occasions in the days following the relaxation of his bail conditions, but each time has been very difficult and he has 'struggled immensely' with the decision to even leave the house."
According to Pistorius's agent, the photo was taken by a "schoolkid on 24 March", then published
in a South African newspaper on Thursday.
The grainy image shows the Paralympian and Olympian on the track wearing his carbon-fibre blades.
"He was just having a jog around his track on his own accord," agent Peet van Zyl told Press Association Sport. "He wasn't back at training."
At London 2012, Pistorius became the first double amputee to run at an Olympics. taking part in both the 400m and 4x400m.
He then won gold medals in the T44 400m and T42-46 4x100m at the Paralympics, as well as silver in the T44 200m.
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