South African police have found a bloodied cricket bat at the home of Oscar Pistorius, a local newspaper reported on Sunday, following the Valentine's Day killing of his model girlfriend.

The star Olympian and Paralympian athlete was charged on Friday with the murder of 29-year-old Reeva Steenkamp, who was shot dead at his luxury Pretoria home in a case that has gripped the world.

His father said in a newspaper interview published on Sunday that there was "zero doubt" his son had mistaken his blonde covergirl girlfriend for an intruder, a suggestion the South African police have dismissed.

Pistorius's family has described the 26-year-old as "numb with shock as well as grief" over the death of Steenkamp, and they rejected the murder allegations.

Police sources close to the investigation told South Africa's independent City Press newspaper that Steenkamp's skull had been "crushed".

"There was lots of blood on the bat," one source said.

Police are investigating whether the bat was used to assault Steenkamp, who was shot four times in the early hours of Thursday, or if she used it to defend herself.

"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 police source told City Press.

The paper said he could have experienced "roid rage", aggressive behavior linked to taking large doses of steroids, describing the case against Pistorius as "rock solid".

Other reports suggested there had been a fight between the two lovers that had spilled over from Wednesday night when neighbors called security guards complaining about a "commotion" inside the Pistorius house.

Police refused on Sunday to comment on the case.

Pistorius, a national icon who inspired people around the world when he became the first double amputee to compete against able-bodied athletes in the Olympic Games last year, is spending the weekend in a police cell.

He is due to apply for bail at a new court hearing on Tuesday, the same day a memorial service will be held for his slain girlfriend. He faces a life sentence if convicted of premeditated murder.

Oscar Pistorius was planning a future with the girlfriend he is accused of shooting dead this week, his uncle said on Saturday.

"They had plans together, and Oscar was happier in his private life than he had been for a long time," Arnold Pistorius said in a statement released by his nephew's agent.

"We are in a state of total shock - firstly about the tragic death of Reeva who we had all got to know well and care for deeply over the last few months," he said. "All of us saw at first hand how close she had become to Oscar during that time and how happy they were."

The suggestion that Pistorius' family was close to Steenkamp runs counter to comments from Pistorius' father, Henke, who told the New York Times he had never met his son's partner.

"I don't discuss my son's relationships. I have, in fact, not met the lady," he was quoted as saying.

Prosecutors alleged the shooting was premeditated, a charge that could put Pistorius behind bars for life if convicted.

Police have said there are no other suspects and the pair were the only people in the house at the time. Initial reports suggested he may have mistaken her for an intruder.

AFP-Reuters