"The minimum that society will be happy with will be 10 years in prison," prosecutor Gerrie Nel said.
'The interest of society demands a prison term'
"This is a serious case."
He was presenting closing arguments during sentencing proceedings for Pistorius, found guilty last month of Steenkamp's culpable homicide.
Nel said he agreed with Barry Roux, for Pistorius, that the athlete be declared unfit to possess a firearm.
He said such agreement "did not happen very often".
Nel rejected argument by Roux that the court should take into account the principles of ubuntu and restorative justice and not send Pistorius to jail.
"It's small things. It's small cases," said Nel, referring to the cases Roux had referred to where these principles had been applied.
"This is not a small case. It's not even a principle that can be considered. The interest of society demands a prison term."
Roux had led evidence by social workers that Pistorius get three years of correctional supervision and 16 hours' community service a month.
The suggestion, as made by the defence, that Pistorius's prosthesis would be taken away in jail should be rejected with contempt, said Nel.
"It's illegal to do so."
On September 12, Judge Thokozile Masipa found Pistorius guilty of the culpable homicide of model and law graduate Steenkamp, but not guilty of her murder. Pistorius had claimed he thought there was a burglar in his toilet when he fired four shots through the locked door in the early hours of February 14 last year, killing Steenkamp.
Masipa found Pistorius guilty of discharging a firearm in public, when he shot from his friend Darren Fresco's Glock pistol under a table at Tasha's restaurant in Melrose Arch, Johannesburg, in January 2013.
Pistorius was found not guilty on two firearms-related charges -- illegal possession of ammunition, and shooting through the open sunroof of a car with his 9mm pistol while driving with friends in Modderfontein on September 30, 2012.