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.

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

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

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.

Police have dismissed initial suggestions that Pistorius, 26, could have mistaken Steenkamp for an intruder, and City Press said 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 fire three more shots," a police source told City Press.

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 after being charged with murder.

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.

Pistorius, who had been going out with Steenkamp since late last year, faces a life sentence if convicted of premeditated murder, as alleged by state prosecutors.

His family have indicated that the star athlete, who broke down sobbing during his initial court appearance on Friday, would plead not guilty.

"We have no doubt there is no substance to the allegation and that the state's own case, including its own forensic evidence, strongly refutes any possibility of a premeditated murder or indeed any murder at all," his uncle Arnold Pistorius said in a statement Saturday.