Stammering and with his jaw trembling, Pistorius told the court he did not intend to kill his 29-year-old lover on Valentine's Day last year.
The Paralympic gold medallist is accused of premeditated murder, but claims he shot the model though a locked toilet door believing she was an intruder.
"I want to take this opportunity to apologise to Mr and Mrs Steenkamp," he said, at times barely audible as he sobbed.
"I was trying to protect Reeva, I want people to know that she was loved when she went to bed that night."
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"I tried to put my words on paper to write to you but no words can ever suffice," he continued.
The athlete cut a broken and emotional figure as he spoke publicly for the first time about events on the night Steenkamp died.
"I've had terrible nightmares," he said since the night of the shooting, adding: "I wake up at night smelling blood."
He also said that since the shooting he has taken sleeping pills and anti-depressants.
After five weeks of prosecution testimony, Monday was the first day of Pistorius's defence.
After calling a pathologist, Pistorius took to the stand, outlining about his problems since the shooting and his early life growing up disabled and without his father present.
"My mother had a lot of security concerns, we grew up in a family where my father wasn't around much, she would often get scared at night, she would phone the police.