Last week, Pistorius began serving a five year prison sentence for the culpable homicide of Reeva Steenkamp, although he could be out in 10 months.
The double-amputee Olympic sprinter was cleared of murder.
"The appeal on conviction is based on the question of law," the national prosecuting spokesman said.
Pistorius' family have said that he will not appeal.
The athlete was also given a three-year suspended sentence for firing a gun in a restaurant.
"The prosecutors are now preparing the necessary papers in order to be able to file within the next few days," Nathi Mncube from the National Prosecuting Authority said in a statement.
Pistorius was charged by the prosecution with the pre-meditated murder of Ms Steenkamp, a model and law graduate.
He was acquitted of this and the lesser murder charge of dolus eventualis.
In South African law, this charge - also known as common-law murder - applies if the accused knew they might kill someone but still went ahead with their course of action.
The BBC's Pumza Fihlani, who followed the athlete's trial, says the prosecution's grounds for appeal may lie with how the judge interpreted dolus eventualis.
The judge's critics have argued that dolus eventualis includes the possibility of meaning to kill one person and ending up killing another, our correspondent says.
Pistorius says he shot dead Ms Steenkamp in the early hours of Valentine's Day last year by mistake, fearing there was an intruder in the house.
On Sunday, Ms Steenkamp's mother June would not say whether the family would support a state appeal.
"All we have ever said is that we want to know the truth. We owe it to Reeva," she told the Times newspaper.
She was interviewed ahead of the publication next month of her book, Reeva: A Mother's Story.
In the book she describes her daughter's boyfriend as "pathetic", "moody", "gun-toting" and "possessive" and rejects his version of events.
"There is no doubt in our minds that something went horribly wrong, something upset her so terribly that she hid behind a locked door with two mobile phones," she writes.
Inside Oscar Pistorius's home
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Mr Pistorius said he and Ms Steenkamp had dinner at about 19:00 before going to bed at 21:00. He said he woke in the early hours, spoke briefly to his girlfriend and got up to close the sliding door and curtains.
Judge Thokozile Masipa questioned the reliability of several witnesses who said they heard screams and gunshots between about 03:12 and 03:17, saying most had 'got facts wrong'.
Mr Pistorius said he heard the bathroom window sliding open and believed that an intruder, or intruders, had entered the bathroom through a window which was not fitted with burglar bars.
Mr Pistorius said he grabbed his firearm and told Ms Steenkamp, who he thought was still in bed, to call the police.
The judge said it made no sense that Ms Steenkamp did not hear him scream 'Get out' or call the police, as she had her mobile phone with her.
Mr Pistorius could see the bathroom window was open and toilet door closed. He said he did not know whether the intruders were outside on a ladder or in the toilet.
He had his firearm in front of him, he heard a movement inside the toilet and thought whoever was inside was coming out to attack him.
'Before I knew it, I had fired four shots at the door,' he said.
The judge said she did not accept that Mr Pistorius fired the gun by accident or before he knew what was happening. She said he had armed himself with a lethal weapon and clearly wanted to use it. The other question, she said, was why he fired not one, but four shots before he ran back to the room to try to find Ms Steenkamp.
Mr Pistorius said he went back to the bedroom and noticed that Ms Steenkamp was not there.
Mr Pistorius said this was when he realised she could have been in the toilet and rushed back to the bathroom.
Mr Pistorius said he screamed for help and went back to the bathroom where he found the toilet was locked. He returned to the bedroom, pulled on his prosthetic legs and turned on the lights before bashing in the toilet door with a cricket bat.
When the door panel broke, he found the key and unlocked the door and found Ms Steenkamp slumped on the floor with her head on the toilet bowl. He then carried her downstairs, where he was met by neighbours.
3D animation of the apartment
South African prosecutors say they are going to appeal against the conviction and sentence given to athlete Oscar Pistorius for killing his girlfriend.