State prosecutor Gerrie Nel said the 27-year-old had consistently changed his version of events and argued that his testimony was "weak".
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Oscar Pistorius in court on Thursday
"The court should have no difficulty in rejecting his full version of events, not only as reasonably possibly true, but in essence as being absolutely devoid of any truth," he stated.
Mr Nel began his closing argument in Pretoria's High Court by stating that Oscar's lawyers had argued two lines of defence that "can never be reconciled".
Prosecutor Gerrie Nel
The sprint runner had claimed he had fired his gun both involuntarily and also out of fear, he argued, adding that the court had to choose one of his defences.
Among those in the packed courtroom for the first time on Thursday were Oscar's estranged father Henke and Reeva Steenkamp's father Barry Steenkamp, who made the trip to join his wife June for the closing arguments.
Reeva Steenkamp's father Barry Steenkamp (right) arriving at court
Oscar has denied murdering his girlfriend Reeva on Valentine's Day of last year, claiming he mistook her for an intruder. The prosecution alleges he deliberately killed her after an argument.
The paralympian's defence lawyer Barry Roux is set to deliver his closing remarks on Friday.
Oscar Pistorius has denied murdering his girlfriend Reeva Steenkamp in February 2013
Judge Thokozile Masipa is then expected to adjourn the trial to consider her verdict – there is no jury.
If found guilty of murder, Oscar could face life imprisonment.