In the statement, from his family and his management company, Pistorius also offered his condolences to the victim's family. "All our thoughts today must be with the family and friends of Reeva Steenkamp," the statement said.
Police were called to Pistorius's home in an upscale, gated community outside Pretoria after neighbours reported screams followed by gunshots in the early hours of Feb 14.
Inside the house was the body of Reeva Steenkamp, a 30-year-old model and law graduate, who had been shot four times in the head and hand. A 9mm revolver was recovered nearby, which police confirmed was registered to Pistorius.
The double amputee popularly known as "Blade Runner", who became the first Paralympian to compete in the Olympics in London last year, was arrested yesterday and spent the night in a Pretoria prison.
Earlier today Pistorius broke down in tears as a court charged him with the murder of his girlfriend. The globally renowned athlete sat hunched as the court heard that prosecutors would argue that the murder was premeditated, a charge that could carry a life sentence.
Pistorius, who runs on prosthetic blades made of carbon fibre, was arrested within hours of the shooting yesterday. He was interviewed by detectives and taken to a nearby police station before going on to a hospital for blood tests and to have swab samples taken from his fingernails.
He was originally due to appear in court yesterday, but the hearing was delayed as police gathered more evidence.
As news of the shooting spread yesterday, it was reported that Pistorius, 26, told police that he had mistaken the woman for a burglar. However, Brig Denise Beukes, a police spokesman, said: "There was no sign of forced entry or persons who weren't supposed to be there at this stage. There were only two people on the premises: the resident and the deceased."
She added that police had been called previously to Pistorius's house at Silver Woods Country Estate to handle "allegations of a domestic nature". Some neighbours are reported to have heard an altercation in the hours before the shots were fired, believed to be at around 4am.
Pistorius heads to the holding cells at the Boschkop police station, east of Pretoria (Reuters)
Henke Pistorius, the runner's father, said last night that he was waiting for news. "We are trying to help as much as we can but there's not much we can do at this stage. It's very difficult to accept when this is your child. We just have to wait and see."
In September 2009, Pistorius spent a night in Boschkop police station, where he was held last night, after he allegedly assaulted a 19-year-old woman during a party at his home. He was not charged but received a caution.
Last September, after Pistorius returned from the Paralympics, he was reported to have exchanged threatening text messages with a businessman whom he considered a love rival. A friend of the man claimed that Pistorius had sent him a text message threatening to break his legs. Police said the matter was resolved amicably and no charges were laid.
In November, Samantha Taylor, Pistorius's former girlfriend of a year and a half, told the South African City Press newspaper that the athlete was "certainly not what people think he is".
She also told Rapport, an Afrikaans newspaper, that she was "prepared to reveal what Pistorius made me go through", but she subsequently withdrew this threat in a lawyer's letter. Her lawyer, June Marks, said she had withdrawn her interview offer after a journalist she had been speaking to started harassing her.
Despite living in a high-security compound, Pistorius told an interviewer recently that he slept with a revolver by his bed, a baseball bat behind his door and a machinegun by the window.
He said in November last year that he went into "full combat recon mode" after mistaking the sound of his washing machine for an intruder.
Pistorius once invited an American journalist to interview him at a shooting range, stating that when he could not sleep, he sometimes went there to fire off his 9mm pistol.
Friends and family of Miss Steenkamp's parents gathered at their home in Port Elizabeth. Samantha Sutton, a close family friend, said the couple were "in a bad way".
Sarit Tomlinson, Miss Steenkamp's agent, said: "She was the kindest, sweetest human being; an angel on earth and will be sorely missed."
South Africa's Olympic committee offered "deepest sympathy and condolences" to the families of Pistorius and Miss Steenkamp.