Ms Steenkamp, a 29-year-old model, was shot dead at Mr Pistorius's home near Pretoria on Thursday.
Appearing in court in Pretoria, Mr Pistorius wept as prosecutors vowed to pursue a charge of premeditated murder.
An application for bail was postponed until next Tuesday and the athlete will remain in police custody.
Dubbed "blade runner", he made history last summer by becoming the first double-amputee track athlete to run in an Olympic Games.
"The alleged murder is disputed in the strongest terms", said a statement released by Mr Pistorius's family and management company after the court hearing.
At the scene
Justine LangBBC News, Pretoria
Irate security guards pushed against the court door as a crowd surged outside. There was simply no more room left. Oscar Pistorius's family squeezed their way in, looking horrified at the line-up of the world's media in front of them.
Then, a sudden hush as the magistrate, Desmond Nair, entered the court. He was not feeling patient: "I want to hear a pin drop in this court."
As Oscar Pistorius was brought in, there was a low-level murmur among the crowd. He cut a dashing but broken figure. His whole body twitched. I was standing so close to him I could see his jawbone slowly grinding.
As the prosecutor told the court he was going for premeditated murder, Pistorius sobbed into his hands. The magistrate asked for him to be seated. His brother, sitting behind him, put a hand on his shoulder.
Throughout the 45-minute session the accused remained silent. This was just the start of what could be a long road ahead.
"Our thoughts and prayers today should be for Reeva and her family - regardless of the circumstances of this terrible, terrible tragedy," it said.
They were the first words released on behalf of the 26-year-old athlete since Ms Steenkamp was found fatally wounded at his home in the gated Silver Woods development outside the South African capital.
But they gave no explanation of what had happened.'Traumatised'
Hours earlier, Mr Pistorius sobbed audibly during his initial appearance at Pretoria Magistrates Court.
Dozens of reporters witnessed the hearing, where chief magistrate Desmond Nair was presiding.
The BBC's Andrew Harding, who was there, said the defendant cut a lonely figure in a crowded court, with his hands clenched and his neck muscles twitching, before he held his head forward, breathing heavily through tears.
When Prosecutor Gerrie Nel argued for the graver charge of "premeditated murder", Mr Pistorius slumped forward at the mention of the words.
If convicted of premeditated murder, the athlete will face a life term in prison. But his defence is seeking a lesser charge, possibly culpable homicide, which is defined in South African law as unlawful, negligent killing.
Media access was discussed at the 40-minute session and the magistrate ruled that there should be no live recording of the bail hearings.
Mr Pistorius's team had argued against such coverage and cited his "extremely traumatised state of mind".
Social networking sites are still flooded with messages of condolence for Ms Steenkamp, but on a much larger scale there has been an overwhelming outpouring of support for the athlete ”
Pumza FihlaniBBC News, JohannesburgA country stunned
Both prosecution and defence agreed Mr Pistorius could remain in custody at a police station and not in prison.
Members of Mr Pistorius's family, including sister Aimee, brother Carl and father Henke, were in the courtroom.
His brother and father, sitting behind the athlete, reached forward to touch his shoulder during the proceedings.
Mr Pistorius had earlier arrived at court in the back of a police vehicle, hiding his face with a jacket and notebook.
Forensic scientists are expected to continue examining the house in the Silver Lakes area on the outskirts of South Africa's administrative capital where Ms Steenkamp, 29, died.
Correspondents say the athlete's arrest has stunned the country where he is considered a national hero.
He is known as "blade runner" because of the carbon fibre prosthetic blades he races in. He was born without a fibula in both legs and had his legs amputated below the knee before his first birthday.
Police were called to his home in the early hours of Thursday morning.
They found paramedics treating a 29-year-old woman with four gunshot wounds to the head and upper body. She died at the scene, and officers recovered a 9mm pistol.
A post-mortem examination was carried out on Friday but the results would not be made public, police said.
Ms Steenkamp's body is due to be flown home to Port Elizabeth for a memorial service next Tuesday, South African media report - the same day that Oscar Pistorius is next expected in court.'Special memories'
They had reportedly been dating since November.
Oscar Pistorius
Popularly known as "blade runner", he was born without a fibula in both legs
Won a key legal battle in 2008, when athletics' governing body, the IAAF, allowed him to compete against able-bodied athletes
Made history in London 2012 by becoming the first amputee sprinter to compete in the Olympics
Apologised after claiming that his rival, Brazilian Alan Oliveira, was wearing blades that were too long in the 2012 Paralympics 200m final
The model was already well known in South Africa but was seen as being on the verge of a new career, with her appearance in a pre-recorded reality TV show set to start on Saturday.
The producers of Tropika Island of Treasure said they were going ahead with the programme, filmed in Jamaica, after "much deliberation".
"Every episode that she is in, every frame that she so ably dominates - shines with her light and her laughter echoes in every conversation, and we want to share these special memories with the rest of South Africa." the programme said.
Meanwhile, world athletics figures spoke of their shock at what had happened.
His training partner, UK 400m runner Martyn Rooney, released a statement saying his "thoughts and prayers go out to the families and friends of those involved".
"I've not heard what he has to say. I wouldn't want to be in his situation, but I hope that, at the end of it all, justice will prevail," said Jamaica's Olympic women's 100m champion Shelly-Ann Fraser-Pryce.
Mr Pistorius dominated in his category at successive Paralympic Games, but in 2008 he won a legal battle over his blades - which critics said gave him an unfair advantage - with the International Association of Athletics Federations (IAAF) for the right to compete in able-bodied competitions.
He reached the 400m semi-finals in the London 2012 Olympics. At the Paralympics he won silver in the T44 200m, gold in the 4x100 relay and gold in the T44 400m, setting a Paralympic record.
South Africa has one of the highest rates of crime in the world and many residents keep weapons to protect themselves against intruders.
But gun ownership is strictly regulated and it is not easy to obtain a licence.
