of Steenkamp, telling a court he shot at her through a locked bathroom door mistakenly believing she was a burglar.
"I am absolutely mortified by the events and the devastating loss of my beloved Reeva," Pistorius said in an affidavit at a court hearing in the capital Pretoria, his first public comments on the killing.
The 26-year-old double amputee Blade Runner track star broke down in tears repeatedly as his own words filled the court: "We were deeply in love and couldn't be more happy."
"I had no intention to kill my girlfriend," he said in the statement read by his lawyer.
As the court hearing proceeded Tuesday, the 29-year-old Steenkamp was laid to rest at an emotional private ceremony at a crematorium in her hometown of Port Elizabeth.
Pistorius was an inspiration to millions when he became the first double amputee to compete against able-bodied athletes in the Olympics in London last year.
He now faces a charge of premeditated murder, which will likely result in remand without bail and, if convicted, a life sentence.
Pistorius said he had awoken in the dead of night early last Thursday when he heard a noise at his upscale Pretoria home
"Filled with horror and fear" that someone was in the bathroom, he said he felt "very vulnerable" because he did not have his prosthetic legs on.
He said he fired shots at the toilet door and shouted to his girlfriend to phone the police, but then realised it could have been Steenkamp in the bathroom.
After smashing the door with a cricket bat, Pistorius said "Reeva was slumped over but alive".
He said he kept a firearm under his bed at night because he had been a victim of violence and burglaries before and had received death threat.
Prosecutors argued that far from being an accident, Steenkamp's death was a premeditated act of murder.
Prosecutor Gerrie Nel told the court Pistorius had armed himself, put on his prosthetic legs, walked seven metres and fired four shots into the bathroom door, hitting a terrified Steenkamp three times and fatally wounding her.
"She could go nowhere," Nel said. "She locked the door for a purpose."
Magistrate Desmond Nair said he could not rule out that there was some planning involved in the killing, which may be considered as a premeditated murder for the purposes of bail.
But Pistorius's legal team rejected the claims as he sought to argue he was not a flight risk.
Pistorius, who off the track has had a rocky private life with stories of rash behaviour, beautiful women, guns and fast cars, has built up a powerful team of lawyers, medical specialists and public relations experts for his defence.
In 2009 Pistorius -- who once admitted to a newspaper that he slept with a pistol, machine gun, cricket bat and baseball bat for fear of burglars -- spent a night in jail after allegedly assaulting a 19-year-old woman at a party.
Meanwhile in Port Elizabeth, tearful friends and family bid farewell to Steenkamp, whose cloth-draped coffin with white flowers laid on top was carried into a chapel in the southeastern coastal city where she grew up.
Pistorius, a Paralympian gold medallist, became the first double amputee to run against able-bodied athletes at last year's Olympics in London on the carbon-fibre running blades that inspired his nickname.
But his career has been put on hold since the shooting, forcing him to cancel races in Australia, Brazil, Britain and the United States between March and May.
Pistorius revealed he earned 5.6 million rand ($640,000) a year and owned the $570,000 house in the gated estate where the killing took place as well as two other homes.
But two of the athlete's American sponsors, Nike and sunglasses maker Oakley, announced they were dropping Pistorius from their advertising campaigns, which have earned him millions of dollars in endorsements.