The hearing has adjourned. A ruling could take a month, although the five-judge panel could choose to expedite the procedure.
Prosecutor Gerrie Nel told the judicial panel that the judge at the trial had made an error of law.
"On the objective facts, the accused cannot escape the conviction of murder," Nel told the judges.
Pistorius, once an athletic golden boy, does not deny shooting Steenkamp to death through his bathroom door, but he has maintained that he thought there was an intruder there.
He was convicted in 2014
of culpable homicide -- a lesser charge than murder -- and sentenced to five years in prison
He was released
after less than a year, to serve the rest of his sentence under house arrest.
Proscutor: Pistorius knew his actions could cause death
Tuesday's hearing in Bloemfontein hinged on the principle of "dolus eventualis," or intent -- the legal principle that the perpetrator foresaw that his act could cause death and went ahead nevertheless.
High court Judge Thokozile Masipa ruled last year that the state had failed to prove that Pistorius intended to kill Steenkamp.
But prosecutors are arguing this was a misapplication of the principle of dolus eventualis, and that Pistorius knew that shooting through the door could cause the death of whomever was inside.
Defense: 'He lacked the intention of illegality'
Pistorius' lawyer rejected that assertion.
"The one factual finding was that Oscar Pistorius was scared and the other that he believed Reeva was in the bed," Barry Roux said. "These cannot be ignored."
"There was no intention to act unlawfully," Roux said. "That was the judge's findings. If there is an absence of illegality then dolus eventualis is not relevant. He lacked the intention of illegality, therefore he couldn't have committed murder."
Roux was questioned far more extensively by the judges than was Nel. But legal experts say nothing can be inferred from that.
Should the prosecutors succeed, Pistorius could be tried again for Steenkamp's killing. A conviction of murder could result in his return to prison.
Pistorius, a double amputee known for his prostheses as the "blade runner
," competed with able-bodied runners in the 400 meters in the 2012 Summer Olympic Games in London.