But the Paralympian's father, Henke Pistorius, said he was certain his son acted ''on instinct'' when he shot and killed Reeva Steenkamp, 29, at his luxury Pretoria home.

South Africa's national broadcaster went ahead with the screening of the reality TV show Tropica Island of Treasure, where a tribute was devoted to slain model Reeva Steenkamp. Photo: AP

Police sources have told the independent City Press newspaper that Ms Steenkamp's skull had been ''crushed''.

''There was lots of blood on the bat,'' one source told the paper.

Investigators have dismissed initial suggestions that Pistorius, 26, could have mistaken Ms Steenkamp for an intruder and City Press reported that she was wearing a nightie at the time of the killing.

''The suspicion is that the first shot, in the bedroom, hit her in the hip. She then ran and hid herself in the toilet … He fired three more shots,'' a source told the paper.

But Mr Pistorius snr, 59, said his family had ''zero doubt'' that Pistorius had shot Ms Steenkamp dead mistakenly thinking she was an intruder.

''When you are a sportsman, you act even more on instinct,'' he said. ''It's instinct - things happen and that's what you do.''

He said the Pistorius family was ''heart and soul'' behind his son and would do ''whatever needs to be done'' to help him clear his name.

His comments followed the family's release of a statement in which they described the athlete as ''numb with shock as well as grief'' over the events of the past three days. They said evidence gathered by the police ''strongly refutes'' any possibility of the premeditated murder charge with which prosecutors have said they will charge the athlete.

They also insisted that Pistorius, whose position as South Africa's golden boy was cemented when he won two gold medals and a silver at last year's London Paralympics, had no reason to harm Ms Steenkamp, his girlfriend of four months.

''All of us saw first-hand how close she had become to Oscar during that time and how happy they were. They had plans together and Oscar was happier in his private life than he had been for a long time,'' they said.

The family fightback came as reports emerged that Pistorius fought to save Ms Steenkamp's life after allegedly shooting her in the early hours of Valentine's Day morning.

Security guards and neighbours who went to his home on a security compound outside Pretoria saw Pistorius running down the stairs with the blonde model in his arms, a source quoted by the Afrikaans newspaper Beeld said.

Ms Steenkamp was still breathing, it said, and Pistorius tried to save her using mouth-to-mouth resuscitation. ''Blood splatters along the route that Pistorius carried her was further proof that her heart was still beating,'' the paper said.

Pistorius has received ‘‘overwhelming support’’ from his fans, his agent says.

Peet van Zyl said outside the Brooklyn police station soon after visiting Pistorius on Sunday that ‘‘a lot of fans’’ had sent their good wishes.

He said the support was ‘‘really on a global scale. South African fans, international fans from literally all over the world.’’

Van Zyl said he visited Pistorius primarily to discuss his running career and would not respond to a question about the mental and emotional state of the 26-year-old athlete.

‘‘I am not going to comment on anything except that (what) is related to his athletics career at this point in time,’’ Van Zyl told reporters.

Van Zyl called Steenkamp’s killing tragic and said he visited Pistorius as a friend as well as an agent.

‘‘Obviously from a management side and also as a friend, it’s a tragic circumstance,’’ Van Zyl said, ‘‘and we can only give Oscar our support at this point in time.’’

He added: ‘‘The nature of my visit was on a professional manner to discuss his career and the plans that we had made for this year with the IAAF (world) championships in Moscow as the main goal for this year.

‘‘We obviously just discussed the races and the contracts that had been signed and secured for this year and also to keep him up to date with regard to the sponsors.’’

Sportswear giant Nike and eyewear manufacturer Oakley are among Pistorius’s big-name sponsors.