The Paralympic athlete killed Reeva Steenkamp in the early hours of Valentine's Day in 2013, saying he mistook her for a burglar when he fired four times through the door of his bedroom toilet.
In March, Pistorius's lawyers failed to reverse an appeal judgement that upgraded his original conviction from culpable homicide -- the equivalent of manslaughter -- to murder.
"It has been very difficult for me to forgive... I feel that Oscar has to pay for what he did. He has to pay for his crime," Barry Steenkamp, 73, said shaking with emotion and in tears.
He also said that he believed the couple had argued on the night of the murder -- disputing Pistorius's claims.
More From This Section
Pistorius held his head in his hands and appeared to be sobbing during the testimony at the High Court in the South African capital Pretoria. Barry Steenkamp, a former racehorse trainer, described the chaos and panic when his wife June rang him at work early in the morning after Reeva, a model and law graduate, was shot.
The original trial judge Thokozile Masipa is due to hand down a new sentence for murder after arguments from both prosecution and defence.
The hearing -- held in the same courtroom as the original trial -- is scheduled to last until Friday. Pistorius faces a minimum 15-year jail term for murder, but his sentence could be reduced due to time already spent in prison and mitigating factors, including his disability.
Pistorius's pastor gave evidence as character witnesses for his defence.
Ebba Gudmundsdottir, from Iceland, told how Pistorius had befriended her family when she was pregnant with a child who would be born without legs.
"He gave us his phone number for us to ask him or consult with him anytime we needed it, which we did and that was lovely," she told the court.
Gudmundsdottir said Pistorius has been an "inspiration" to her son, and they had gone to see him compete three times in the Paralympics. Pistorius once gave her son a gold medal and said "This is for you champion".
Another witness, prison nurse Charlotte Mashabane, alleged that Pistorius had been a difficult inmate and had argued with officials, shouting and banging her desk in a dispute over medication.
Barry Roux, defence lawyer, accused her of giving contradictory evidence and exaggerating his behaviour due to a personality clash.
Pistorius has always denied killing Steenkamp in a rage and, during his seven-month trial in 2014, vomited in the dock as details of his lover's death were examined in excruciating detail.