Police find blood-covered cricket bat at Pistorius's home

South African police have found a bloodied cricket bat at the home of Oscar Pistorius, a local newspaper reported on Sunday.

The Olympian athlete was charged on Friday with the murder of his model girlfriend 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, according to AFP.

Police are probing if 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 fired three more shots," a police source told City Press.

Pistorius 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 would plead not guilty, a family source said.