But he said he did not mean to kill her, and protested the charges against him.
"I fail to understand how I could be charged with murder, let alone premeditated murder because I had no intention to kill my girlfriend," Pistorius said in the statement.
"We were deeply in love and couldn't be happier," he said."I loved her and I know she felt the same way."
A premeditated murder?
Prosecutors, however, painted a different picture.
They rejected Pistorius' claim that he mistook her for a burglar, saying it would make no sense for an intruder to hide behind a locked bathroom door.
Instead, they say Pistorius armed himself, attached his prosthetic legs and walked 7 meters (23 feet) to shoot Steenkamp through a bathroom door after a heated argument.
Defense attorney Barry Roux questioned the state's argument, asking how prosecutors would know Pistorius had put on his prosthetic legs and walked to the bathroom before shooting his girlfriend.
Police were alerted to the shooting by neighbors, and residents had "heard things earlier," police spokeswoman Denise Beukes said.
Authorities said there had been "previous incidents" at the home, including "allegations of a domestic nature," but did not provide details.
Detectives are investigating the blood-stained cricket bat found in the home, Johannesburg's City Press newspaper reported. They are trying to determine whether it was used to attack Steenkamp, if she used the bat in self-defense, or if Pistorius used it to try to break down the bathroom door, the newspaper said.
Final farewells for Steenkamp
As the drama in court unfolded, friends and family mourned Steenkamp at a private funeral in her hometown of Port Elizabeth.
"There's a space missing inside all the people she knew that can't be filled again," her brother Adam Steenkamp told reporters outside.
Steenkamp was a law school graduate whose modeling career was on the rise. She landed the cover of FHM magazine and recently appeared on a reality TV show.
On Sunday, South Africans heard Steenkamp's voice one last time after her death, when the national broadcaster aired a pre-recorded episode of the show. The model talked about her exit from "Tropika Island of Treasure," on which local celebrities compete for prize money.
"I'm going to miss you all so much and I love you very, very much," she said, blowing a kiss to the camera.
Case rivets fans
The case of the global sports hero known as the "Blade Runner" has riveted stunned fans around the world.
As he walked into court in a blue shirt and gray suit, frenzied photographers snapped away, prompting the judge to demand they stop.
The scene was a far cry from the packed stadiums that erupted in applause whenever the double-amputee competed against men with legs.
On social media, sentiment appeared to mixed. "Oscar Pistorius is telling us rubbish," one Twitter user posted.
But others were more supportive after hearing Pistorius' story. "I for some reason believe Pistorius after reading his affidavit!!," another person tweeted.