DNA tests from a headless torso found in the Baltic Sea matches with missing Swedish journalist Kim Wall, Danish police say.

Ms Wall, 30, was last seen alive on August 10 on Danish inventor Peter Madsen’s submarine, which sank off Denmark’s eastern coast the day after.

Mr Madsen, who was arrested on preliminary manslaughter charges, denies having anything to do with Ms Wall’s disappearance.

The headless torso was found by a cyclist on Copenhagen’s southern Amager island on Monday, near where she was believed to have died.

Copenhagen police said the arms and legs had been “deliberately been cut off” the body.

Police investigator Jens Moeller Jensen said the body was attached to a piece of metal, “likely with the purpose to make it sink”.

The body “washed ashore after having been at sea for a while,” he said on Wednesday.

There were marks on the torso, indicating someone tried to press air out of the body to stop it floating, Mr Moeller Jensen added.

Peter Madsen has been charged with manslaughter. He denies the charges. Photo: AAP

“On August 12, we secured a hair brush and a toothbrush to ensure her DNA. We also found blood in the submarine and there is a match,” Mr Jensen said.

The cause of the journalist’s death is not yet known, police said.

Mr Madsen, who remains detained in police custody, initially told police that she disembarked from the submarine to a Copenhagen island several hours into their trip and that he did not know what happened to her afterward.

He later told authorities that “an accident occurred onboard that led to her death” and he “buried” her at sea.

My friend Kim Wall has gone missing on Friday in Copenhagen. If you have any info please contact Danish police. https://t.co/SUv0N3JjHY pic.twitter.com/3e9ScqX6W4

— Marie Telling (@MarieTelling) August 11, 2017

Ms Wall was reported missing by her boyfriend Bo Peterson around 2.30am on Friday.

The journalist was working on a story about Mr Madsen, her family told Associated Press.

Mr Madsen was rescued after the submarine sank. There was no body inside it and Mr Moeller Jensen had speculated early in the investigation that it might have been deliberately sunk.

Ms Wall was a freelance journalist who had written for The Guardian, New York Times and South China Morning Post.

Ms Wall’s family expressed “boundless grief” after receiving the news of her death.

“We can’t fathom the scope of the disaster, and many questions remain to be answered,” Ms Wall’s mother Ingrid Wall, wrote on Facebook.

Ingrid said that the family had received numerous messages of support during the days that passed her daughter disappeared, showing “how loved and appreciated she was, as a person and a professional reporter”.

-with agencies