The Paralympian is facing a charge of murder after Steenkamp was found shot dead at his Pretoria home on Thursday, February 14.
State prosecutors had argued that Pistorius had put on his prosthetic limbs and walked seven metres before firing four shots - with three fired from the opposite side of a closed bathroom door.
Prosecutor Gerrie Nel rejected the suggestion that Pistorius mistook Steenkamp for an intruder and argued that premeditation need not require weeks or months of planning.
Defence lawyer Barry Roux told the court that the team gave "no concession that this is even murder" and that Pistorius did not know his girlfriend was the person behind the bathroom door.
After a short break in the session, chief magistrate Desmond Nair ruled that the case was a schedule six offence as he could not completely rule out premeditation.
This means that the defence has to prove "exceptional circumstances" for the athlete to be granted bail.
Pistorius cried as the announcement was made - and his family then wept, grouped together in a circle.
After further legal arguments were made, Roux read the following statement from Pistorius: "I fail to understand how I could be charged with murder, let alone premeditated murder, as I did not intend to kill my girlfriend Reeva Steenkamp."
He added that he was not a flight risk because he loves South Africa. He noted that his house is valued at 5 million rand (£366,077) with other properties valued at 2 million.
As Roux recounted Pistorius's version of the events on February, magistrate Nair paused the reading of the statement when Pistorius wept uncontrollably.
According to the statement, Pistorius and Steenkamp were "deeply in love". She had bought him a gift for Valentine's Day.
Through his lawyer, Pistorius explained that he had been the victim of crime in the past and has also received death threats, causing him to sleep with a 9mm gun under his bed.
On hearing a noise in the bathroom after going to the balcony, he felt vulnerable as he had not attached his prosthetic limbs. With the lights off, he thought Steenkamp was in the bed.
He yelled at the suspected intruder and, feeling vulnerable, fired several shots through the bathroom door. On noticing that Steenkamp was not in the bed, he realised that she may have been in the bathroom.
Pistorius then screamed for help, put on his legs, kicked the door in and saw his girlfriend - still alive - slumped over the toilet. He then called for paramedics and tried to take her to hospital.
"I trust the South African legal system and the facts will show that I did not murder Reeva," Pistorius's statement continued.
"I tried to save Reeva. But she died in my arms. I can't stand how much hurt I've caused."
He added that he was an international sports star who would not evade his trial, adding that he would not interfere with witnesses and would be willing to surrender his passports.
After several statements were read in support of Pistorius by friends, the defence concluded its arguments in favour of bail - but wanted the option of further arguments once they receive certain information from prosecutors.
The court adjourned until tomorrow (February 20), 9am local time, and Pistorius will be held for another night at Brooklyn police station.
Steenkamp's private funeral was held this morning in Port Elizabeth.
Gallery - Oscar Pistorius in pictures: