Initially, Madsen claimed he'd dropped Swedish journalist Kim Wall off before the sinking and he didn't know where she was.

Now police say Madsen has admitted that Wall died in an accident on his sub and he "buried her at sea."

Madsen was found on August 11th by the Danish Navy following a search for the missing submarine. He initially claimed that he'd dropped Wall off on the shore in Copenhagen Bay on August 10th. Her boyfriend was the first to alert the police that the sub was missing. He told authorities that Wall had left with Madsen in the vessel and had not returned on time. He explained that she was writing a story about the renaissance man for Wired magazine.

Body found as Danish submarine man says missing woman died on board

A headless female torso was found on Monday in the water's edge in Copenhagen, hours after a Danish inventor charged with killing a journalist in his home-made submarine told a court she died on board, police said.

Peter Madsen told the court that Swedish journalist Kim Wall had died in an accident and he had buried her at sea, changing his earlier statement the he dropped her off alive in Copenhagen.

Police later told a press conference that it was still too early to identify the body - missing its head, legs and arms - that was found by a passing cyclist.

Update:

"The body bears the mark of having, most likely, been inflicted deliberate damage with the purpose of ensuring that gasses can pass out of the body -- possibly in an attempt to avoid that a body rises from the seabed," Møller said. [...]

Danish police said that in light of the findings they would look afresh into unsolved cases such as the murder of a Japanese tourist in 1986. Body parts of 22-year-old Kazuko Toyonaga were found in plastic bags at separate locations in the waters outside Copenhagen almost a month after the student disappeared on her travels through Scandinavia.

Update 2:

Divers found bags containing her head, legs and clothing in Koge Bay, just south of Copenhagen, the city's police inspector Jens Moller Jensen said. [...] "In the same bag laid a knife, and there were some car pipes to weigh the bag down," he said. [...]

Danish Prosecutor Jakob Buch-Jepsen told a court earlier this month that footage of women being decapitated alive had been found on a hard drive believed to belong to Mr Madsen.