Magistrate Desmond Nair on Tuesday added there was no evidence to rule out premeditated murder.
"I cannot at this point completely exclude planning," he said.
As the funeral of Steenkamp began in Port Elizabeth on Tuesday, allegations on her death emerged at Pistorius's bail bid.
After days of frenzied speculation and leaks in the media about what might have happened, state prosecutor Gerrie Nel went straight to the point at the Pretoria Magistrate's Court.
He repeated last week's submission that the state believed her death was premeditated murder.
Nel said Pistorius put on his prosthetic legs, walked to his bathroom and fired four shots, three of which hit Steenkamp.
"He prepared. He armed himself. The motive was: he wanted to kill," Nel alleged.
He rejected Pistorius's version that he mistook Steenkamp for a burglar and said there was no evidence to support this.
Nel said: "We say this in itself constitutes premeditated murder of a burglar."
He submitted that Steenkamp arrived at Pistorius's home, at the Silver Woods country estate in Pretoria, between 5pm and 6pm on Wednesday night, February 13.
Pistorius kept his eyes downcast as Nel said there were two people in the house. Steenkamp's overnight bag was there and a cosmetic bag was left in the bathroom.
Nel said Pistorius, a double amputee who became an Olympic athlete, walked seven metres to the bathroom, which measured 1m by 1.14m.
The state would argue that the bathroom door was locked. It wanted to know why a burglar would lock himself in a bathroom.
Nel said the bathroom door was broken down and according to blood spatter analysis, Pistorius picked Steenkamp up and carried her downstairs.
Security guards were outside the house and a discussion started.
Pistorius told a friend he had thought Steenkamp was a burglar, Nel told the court.
Pistorius's lawyer Barry Roux, told the magistrate the state could not prove that Pistorius knew Steenkamp was on the other side of the bathroom door.
If needed, evidence would be brought of men who had shot their wives or children thinking they were burglars, Roux said.
He would also, if necessary, bring evidence of burglaries and robberies at security complexes.
A teary-eyed Pistorius watched while Roux said: "We submit it's not even murder."
"There's no agreement there, not even concession that this is murder," said Roux.
Meanwhile, mourners were attending Steenkamp's private funeral at the Victoria Park Crematorium in Port Elizabeth. They included Springbok rugby player Francois Hougaard and pupils of St Dominic's High School, which Steenkamp attended. – Additional reporting by Sapa