Sources close to the investigation told the South African newspaper City Press there were no signs of forced entry, and that the first shot was fired in the bedroom, before Pistorius' girlfriend Reeva Steenkamp locked herself in the bathroom.
Pistorius, an Olympic runner with double below-knee amputations, allegedly shot and killed his girlfriend Reeva Steenkamp on Thursday
City Press also revealed a bloodied cricket bat is the central piece of evidence in the investigation, but did not say why.
Meanwhile, Pistorius' father, Henke Pistorius, 59, says his son fatally shot his girlfriend "on instinct" and must have mistaken her for an intruder, the British newspaper The Sunday Telegraph reported.
"When you are a sportsman, you act even more on instinct," Pistorius' father, Henke Pistorius, 59, said. "It's instinct -- things happen and that's what you do."
Henke Pistorius' comments came after the entire Pistorius family put out a statement in which the younger Pistorius is described as as "numb with shock as well as grief" over the events of the past three days.
The family claims Pistorius, 26, had no reason to harm Steenkamp, 29, his girlfriend of four months.
"All of us saw at 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," the statement said.
Oscar Pistorius was the first amputee runner to compete at an Olympic Games. He went on to win two gold medals and a silver at last year's London Paralympics.