Oscar Pistorius is not back in official training and is "still in an extremely traumatised state", his family said.
His uncle Arnold Pistorius said in a statement that although the 26-year-old had been out running, he is not on any "official training programme".
The statement followed the publication in a South African newspaper of Pistorius running round a track in Pretoria.
The photograph, taken by a member of a children's hockey team, shows the 2012 Paralympic gold medal winner wearing his blades and jogging around the track at the University of Pretoria.
Pistorius is awaiting trial for the alleged murder of his girlfriend Reeva Steenkamp in February. The double amputee and six-time Paralympic sprint champion has been charged with premeditated murder, but claims he shot 29-year-old Ms Steenkamp after mistaking her for an intruder.
He is next due in court on June 4, with a trial expected to take place before the end of this year. Last week his bail conditions were changed by a judge, allowing him to travel abroad providing he hands over his travel plans.
The changes mean Pistorius could attempt to qualify for August's World Athletics Championships in Moscow, although it is thought unlikely that he will be invited to take part in the London Anniversary Games at the end of July.
But in his statement, Arnold Pistorius quashed rumours that his nephew is back in training, saying: "Oscar is not back on any official training programme. This may change in future, but this will be a decision taken by Oscar, and Oscar alone.
"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 where various family members and his trainer were present. We all encouraged him to get back onto the track to help stabilise him emotionally."
"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."