Danish inventor Peter Madsen on Thursday denied murdering Swedish journalist Kim Wall aboard his self-built submarine on the first day of his highly-anticipated trial, as the prosecution painted a picture of a sexual sadist obsessed with beheadings.

Madsen, who has previously admitted dismembering Wall's body and throwing her remains overboard, did not address the court but his lawyer Betina Hald Engmark said he denied the murder charge and maintained that the 30-year-old freelance reporter died accidentally on board his submarine.

Wearing a black T-shirt and jeans, Madsen appeared calm in the Copenhagen district court, his gaze often looking downwards as Wall's parents sat nearby.

The trial, scheduled to last until April 25, is expected to shed more light on the circumstances of Wall's grisly death on Madsen's Nautilus submarine in August last year, when she vanished after going for an evening sail with him to interview him for an article.

Her chopped up body parts, weighed down in plastic bags with metal objects, were later recovered from Danish waters off Copenhagen.

Prosecutor Jakob Buch Jepsen has previously said he will seek a life sentence, which in Denmark averages around 16 years, against Madsen, an eccentric semi-celebrity in Denmark who built rockets and dreamed of developing private space travel.

He faces charges of premeditated murder, desecrating a corpse, and aggravated sexual assault.

Different event versions

Wall was reported missing by her boyfriend after she failed to return home from her trip on the 60-foot (18-metre) vessel on August 10.

That evening, the couple were having a going-away party -- they were due to move to China a few days later -- when Madsen, whom she had been trying to interview, contacted her and invited her out to the sub.

On a large screen in the courtroom, the prosecutor showed a series of text messages Wall sent her boyfriend from inside the vessel.

"I'm still alive btw (by the way)," she wrote, adding: "But going down now!" and "I love you!!!!!!"

A minute later, she added: "He brought coffee and cookies tho."

Madsen has changed his version of what happened several times, first saying he dropped her off, then that she hit her head on the hatch, then suggesting she may have died of carbon monoxide poisoning.

He has continued to insist her death was an accident but provided no explanation.

An autopsy was unable to determine her cause of death, nor has a motive been established.

But prosecutors argued Thursday that Madsen killed Wall as part of a sexual fantasy.

They cited a psychological assessment which declared him "highly unreliable, a perverted polymorph, and highly sexually deviant".

"He has narcissistic and psychopathic traits, and is manipulating, with a severe lack of empathy and remorse," Buch Jepsen said.

Prosecutors say Madsen bound Wall by the head, arms and legs before beating her and stabbing her repeatedly in her genital area.

They say he then killed her -- probably strangling or slitting her throat -- and cut her up with a saw, stuffing her torso, head, arms and legs in separate bags weighed down with metal objects, and dumping them in Koge Bay off Copenhagen.

Madsen previously told investigators he panicked after her accidental death, and dismembered her and buried her at sea.

Decapitation videos

Prosecutors introduced as evidence a hard drive seized in his workshop containing fetish films, in which women were tortured, decapitated and burned alive.

Seven texts "about impalement of women, mostly in the genitals" were also found.

Madsen has said the hard drive was not his.

Investigators never found Wall's or Madsen's phones, but were able to recreate some of the messages on them.

On the morning of August 10, Madsen "googled 'beheaded girl a(r)gony' which leads to a video of an unidentified young woman who is slowly having her throat cut," the prosecutor said.

On July 26, he also googled "female beheading" and watched the videos.

Buch Jepsen told the court forensic evidence of Wall "shows that her lungs reacted as they would if air supply suddenly stopped, which would be due to either beheading or strangulation".

Madsen's defence lawyer said the prosecution case didn't hold up, and emphasised that the cause of death had not been determined.

"The prosecution's statement has some holes," Hald Engmark told the court.

"If these statements as presented by the prosecutor can be proven, it would be very incriminating for my client. However there is not enough proof."