PRETORIA (Reuters) - "Blade Runner" Oscar Pistorius put on his artificial legs and walked across his bedroom before firing four handgun rounds into the locked bathroom door, killing his cowering girlfriend in cold blood, prosecutors said on Tuesday.

Reeva Steenkamp, a law graduate and model, died after being hit by three rounds, prosecutor Gerrie Nel said.

Pistorius wept uncontrollably in court as Nel outlined details of a shooting that has gripped South Africa and the millions around the world who saw the double amputee's track glory as the ultimate tale of triumph over adversity.

Scores of mourners gathered in the coastal city of Port Elizabeth for Steenkamp's funeral, where the mood was one of grief tinged with anger at the loss of "an angel".

In Pretoria central magistrate's court, defense lawyer Barry Roux disputed the murder charge, saying the facts surrounding the shooting in the early hours of Thursday were unclear.

"All we really know is she locked herself behind the toilet door and she was shot," he told the packed courtroom.

However, Nel, his opposite number at the bail hearing, painted a picture of premeditated killing - a crime that carries a life sentence in South Africa.

"If I arm myself, walk a distance and murder a person, that is premeditated," he said. "The door is closed. There is no doubt. I walk seven meters and I kill."

"The motive is 'I want to kill'. That's it," he added. "This deceased was in a 1.4 by 1.14 meter little room. She could go nowhere. It must have been horrific."

The arrest of Pistorius, 26, stunned the millions who had watched in awe last year as the Olympic and Paralympic sprinter reached the semi-final of the 400 meters in the London Olympics, running on high-technology carbon fiber 'blades'.

Initial reports suggested he might have mistaken Steenkamp for an intruder - a possibility in crime-ridden South Africa and a version Pistorius told his sister immediately after the shooting, Nel said.

The prosecution countered this theory by saying Steenkamp's overnight bag had been found in the bedroom of the plush two-storey home in a gated compound north of Pretoria.

"ROT IN JAIL"

Dressed in a dark suit, Pistorius arrived at the court in a police car shortly before 7 a.m. (0500 GMT). Proceedings were delayed as more than 100 journalists from around the world jostled to get into the dimly lit, brick-face courtroom.

The case has drawn further attention to endemic violence against women in South Africa after the gang-rape, mutilation and murder of a 17-year-old near Cape Town this month.

Members of the Women's League of the ruling African National Congress protested outside the building, waving placards saying: "No Bail for Pistorius" and "Rot in jail".

At Steenkamp's cremation in the windswept Victoria Park Crematorium in Port Elizabeth, sorrow mingled with outrage.

"She was an angel. She was so soft, so innocent. Such a lovely person. It's just sad that this could happen to somebody so good," said Gavin Venter, an ex-jockey who worked for Steenkamp's father.

"I'm disgusted with what he did. He must be dealt with harshly," he added. "Without a doubt he's a danger to the public. He'll be a danger to witnesses. He must stay in jail."

After the hour-long private ceremony in the cream-colored hill-top church, Steenkamp's brother Adam and uncle Mike, fighting back tears, spoke briefly to reporters.

"There's a space missing inside all the people that she knew that can't be filled again," Adam Steenkamp said. "We are going to keep all the positive things that we remember and know about my sister. We will miss her."

The case has gripped sports-mad South Africa, where Pistorius was seen as a rare hero who had transcended the racial divides that persist 19 years after the end of apartheid.

Pistorius' endorsements and sponsorships, which include sportswear giant Nike, British telecoms firm BT, sunglasses maker Oakley and French designer Thierry Mugler, are thought to be worth as much as $2 million a year.

Nike said on Monday it had dropped Pistorius from any future advertising campaigns. Other sponsors have said they will make no decisions until the legal process has run its course.

Pistorius has cancelled scheduled track appearances in Australia, Brazil and Britain in the coming months to focus on his attempt to clear his name.

Born without a fibula in either leg, Pistorius had his lower legs amputated as an 11-month-old baby but became the highest-profile athlete in the history of the Paralympic Games.

In last year's Paralympics he suffered his first loss over 200 meters in nine years. After the race he questioned the legitimacy of Brazilian winner Alan Oliveira's prosthetic blades, but was quick to express regret for the comments.