The double-amputee athlete killed Reeva Steenkamp in February 2013 after firing four times through a locked toilet door.
A manslaughter verdict was overturned last month and a murder verdict introduced in its place.
Oscar Pistorius’ defense has lodged papers at the Constitutional Court, urging a review of his murder conviction.
The champion is currently under house arrest after spending one year of his original five-year sentence in jail.
South Africa’s Supreme Court of Appeal ruled in December that the lower court had not applied correctly the rule of dolus eventualis – whether Oscar Pistorius knew that a death would be a likely result of his actions.
Last month, Justice Eric Leach said that having armed himself with a high-caliber weapon, Oscar Pistorius must have foreseen that whoever was behind the door might die, especially given his firearms training.
Oscar Pistorius has always maintained he believed he was shooting at an intruder.
His lawyers say the appeals court made fundamental errors, claiming in appeal papers that the court “acted unlawfully and unconstitutionally when it rejected the factual finding of the Trial Court and replaced it with a contrary factual finding of its own”.
Oscar Pistorius’ lawyer, Andrew Fawcett, says the appeal is now in the hands of the director of public prosecutions, who must decide whether there are grounds for appeal.
If so, the case will go before the Constitutional Court.
Oscar Pistorius made history by becoming the first amputee sprinter to compete at the Olympics, in London in 2012. He competed in the 400m, wearing carbon-fiber blades to run against able-bodied athletes.
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