What sparked the shooting remained unclear, but police said they had received calls in the past about domestic altercations at the home of the 26-year-old athlete, who has spoken publicly about his love of firearms.
A police spokeswoman, Brigadier Denise Beukes, said the incidents included "allegations of a domestic nature."
"I'm not going to elaborate on it, but there have been incidents," Beukes said. She said Pistorius was home at the time of Steenkamp's death and "there is no other suspect involved."
Pistorius made history in the London Games when he became the first double-amputee track athlete to compete in the Olympics. He didn't win a medal but did make the semifinals of the 400 meters and became an international star.
Thursday, companies quickly removed billboards and advertising featuring Pistorius, a national hero in South Africa who also inspired fans worldwide with the image of his high-tech carbon-fiber blades whipping through the air.
Kenny Oldwage, Pistorius' lawyer, told reporters the athlete was "emotional" after his arrest, "but he is keeping up." He said he planned to seek bail for Pistorius at a preliminary hearing Friday.
Pistorius has had troubles in the past in his personal life, which often featured fast cars, cage fighters and women.
In February 2009, he crashed a speedboat on South Africa's Vaal River, breaking his nose, jaw and several ribs and damaging an eye socket. He required 180 stitches to his face. Witnesses said he had been drinking, and officers found alcoholic beverages in the wreckage, though they did not do blood tests.
In November, Pistorius was involved in an altercation over a woman with a local coal mining millionaire, South African media reported. The two men involved the South African Police Service's elite Hawks investigative unit before settling the matter.
Pistorius' father, Henke Pistorius, said Thursday: "We all pray for guidance and strength for Oscar and the lady's parents."
A spokeswoman for Pistorius at Fast Track, an international sports marketing agency in London, said the athlete was assisting with the investigation and there would be no further comment "until matters become clearer."