Prosecutors say Pistorius was often jealous and overbearing in his relationship with Ms Steenkamp and killed her intentionally after a loud argument in the pre-dawn hours of Valentine's Day last year.
Pistorius claims he shot the 29-year-old model by mistake through a toilet door at his house, thinking she was a dangerous intruder.
Pistorius referred to a phone message Ms Steenkamp sent him in late January 2013 when she said she was sometimes "scared" of the double-amputee Olympic athlete. The prosecution presented the message earlier in the trial as an indicator of Pistorius's threatening behaviour.
Pistorius, 27, said that the couple had a disagreement at a social function that day and he was "maybe just being sensitive, insecure or jealous". Pistorius said he apologised to Ms Steenkamp and sent her a message saying: "I want to talk to you. I want to sort this out. ... I'm sorry for the things that I say without thinking."
"My lady, I think it was a bad day in our relationship," Pistorius said, addressing the judge who will ultimately deliver a verdict in the trial that began last month in Pretoria.
Defence lawyer Barry Roux asked Pistorius if the unhappiness in their relationship had passed and Pistorius replied yes.
Pistorius was being led through questions by Mr Roux, with the defence attempting to counter accusations that the runner was a reckless hothead with an obsessive love of firearms and prone to outbursts of anger.
Speaking softly, Pistorius mostly kept his composure, with his voice occasionally quivering with emotion when he spoke about the woman he killed by shooting her three times, in the head, arm and hip.
He also spoke of the first time he met Ms Steenkamp, in November 2012, and his decision to ask her to join him at a sports awards event that evening on the spur of the moment. He denied he had cheated on a former girlfriend when he met Ms Steenkamp, saying the previous relationship had ended.
Pistorius first took the witness stand on Monday, making a tearful apology to Ms Steenkamp's family for killing her as Ms Steenkamp's mother, June, sat in the courtroom, staring at him without expression.
Pistorius faces 25 years to life in prison if convicted on the murder charge.