Lukasz Czapla has admitted withholding information when being interviewed about killing his son "because he could not confront his actions".
The 41-year-old is on trial accused of murdering his two-year-old boy, Julius, at his home in Muirhouse, Edinburgh, in November 2020.
Former IT technician Lukasz has offered to plead guilty to culpable homicide - but this was not accepted by the Crown.
The court previously heard Czapla told police officers and psychiatrists that he could not remember killing his son days after the toddler's body was found.
But a couple of months later, after claiming to remember more details, the accused then gave a "harrowing" account of how he killed the boy, according to consultant psychiatrist, Dr Alexander Quinn, who has previously given evidence at the trial.
At the High Court in Edinburgh on Friday, Czapla admitted to initially lying to psychiatrists about what he had done.
Iain McSporran QC, defence, asked the accused: "When you initially told them you could not remember, is it because you couldn't remember or because you couldn't face it?"
Czapla replied: "I didn't want to face it."
McSporran then asked if Czapla was lying, to which he said: "Yes, you could say I was lying when I said I couldn't remember.
"I couldn't face it."
Reflecting on this, the accused started crying in the dock, adding: "It was soul destroying."
Ealier, the court had heard Czapla and his former partner, Patrycja Szczesniak, the mother of Julius, had relationship issues, particularly after their seven-year relationship ended in June 2020.
Mr McSporran asked Czapla if he wanted Julius to die to "punish" Ms Szczesniak, to which he replied: "No."
He was then asked if the killing was due to "wickedness against Julius", to which Czapla said: "No, I had nothing against Julius, he was the love of my life, he was my best friend."
The accused then broke down in tears in court.
Earlier, the jury heard Czapla lost his father, whom he described as his "best friend", at a young age.
He told the court he saw his father's body, and the death left him with "a massive emptiness".
Czapla said he suffered with mental health problems from a young age, and the day Julius was found dead he had tried to kill himself.
When the defence asked if he had any thoughts about his son at the time, he said: "I didn't see any point in living and I thought about him (Julius), he relied on me.
"I didn't want to leave him alone.
"I remember my father's dead body and I thought Julius will have to see this, too, and so I thought I will have to take him with me."
McSporran asked Czapla to clarify if "take him with me" meant killing Julius, to which the accused replied: "Yes."
Czapla was asked if he "welcomed fatherhood" when Julius was born, to which Czapla said: "Yes, it was the best time of my life.
"The happiness and strength of a parent can overcome obstacles, you can do anything."
When asked if his son was happy to see him whenever they were together, Czapla, between tears, replied: "Yes, he would shout, 'daddy' and run into my arms."
Earlier, toxicology and police evidence showed that Czapla was intoxicated at the time of Julius's death, having drunk alcohol and consumed anti-depressant medication.
Czapla denies murdering the toddler in his home in November 2020.
He has pleaded guilty to nine other charges which include dangerous driving, drug possession and having an air weapon.
The trial, before Lord Beckett, continues.
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