South Africa's prosecutors have sought permission to appeal against athlete Oscar Pistorius' "shockingly light" sentence, court papers show.
Last month, Pistorius began serving a five year prison sentence for the culpable homicide of Reeva Steenkamp, although he could be out in 10 months.
The sentence failed to consider the "horrendous manner" in which Ms Steenkamp was killed, prosecutors said.
Prosecutors are also appealing against Pistorius' murder acquittal.
The double-amputee Olympic sprinter was charged by the prosecution with the pre-meditated murder of Ms Steenkamp, a model and law graduate who was his girlfriend.
He was acquitted of this and the lesser murder charge of dolus eventualis by High Court Judge Thokozile Masipa on 21 October.
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 appeal on conviction is based on the question of law," said National Prosecuting Authority spokesman Nathi Mncube in a statement.
In papers filed with the North Gauteng High Court and published by South Africa's Eyewitness News on its website, prosecutor Gerrie Nel said Judge Masipa "erred in over-emphasising the personal circumstances of the accused and the fact that the accused was suffering from post-traumatic stress, was anxious and 'seems remorseful'.
"Not enough emphasis was placed on the horrendous manner in which the deceased died coupled with the gruesome injuries she sustained when the accused shot and killed her," he said.
Pistorius' sentence was "shockingly light, inappropriate and would not have been imposed by any reasonable court", Mr Nel added.
The judge failed to sufficiently consider that Pistorius acted with "gross negligence", and had fired four shots with a gun "loaded with black talon ammunition through a locked door into a small toilet cubicle from which there was no room to escape".
The prosecution had called for him to be given the maximum 15-year sentence for culpable homicide, or manslaughter.
Ms Steenkamp was killed at Pistorius' upmarket home in the capital, Pretoria, in the early hours of Valentine's Day last year.
He said he feared there was an intruder but he did not intend to kill.
Mr Mncube said the application for permission to appeal was expected to be considered by Judge Masipa.
"If it's granted, the case will then be heard by the Supreme Court of Appeal," Mr Mncube is quoted by AFP news agency as saying.
Prosecutors had the option to petition the Supreme Court to hear the case if permission was refused, Mr Mncube said.
The athlete was also given a three-year suspended sentence for firing a gun in a restaurant.
Pistorius is currently serving his sentence in the hospital section of Pretoria's Kgosi Mampuru II jail.
He can apply to serve the rest of his sentence under house arrest after 10 months in prison.
After the verdict, his family said that he would not appeal.
Inside Oscar Pistorius's home
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