In initial police questioning, Madsen, who is suspected of her death, had denied cutting up her body and said she died in an accident when a heavy submarine hatch fell on her head.
He has now changed his story to say she died of carbon monoxide poisoning while on board, police said in a statement.
“He has now explained that Kim Wall died as a result of carbon monoxide poisoning inside the submarine at a time when he was on deck,” police wrote.
“Furthermore, Peter Madsen has admitted that he subsequently dismembered her corpse and disposed of the body parts in Køge Bay,” the statement continued.
“This version of events naturally requires police to gather diverse supplementary statements from forensic specialists and submarine experts,” lead investigator Jens Møller Jensen said.
Madsen, 46, has also voluntarily extended his preliminary detention until November 15th, Copenhagen Police confirmed via press statement.
His detention on suspicion of killing Kim Wall has already been extended twice and had been due for review on October 31st.
Wall, a freelancer based in China and New York, never returned from her interview with Madsen on August 10th.
Her torso was found floating in Køge Bay on August 21st, and her head, legs and clothes were recovered in plastic bags in the same waters on October 7th.
Madsen, a self-taught engineer and inventor, has been held in custody on suspicion of killing Wall since August 11th and has now changed his version of events twice.
He denies killing the 30-year-old journalist.
After intentionally sinking his submarine early on August 11th in Køge Bay, he was picked up by a rescue vessel and told police he had dropped Wall off on land after their interview the previous evening.
The following day, he changed his story to say a 70-kilo (154-pound) hatch fell on her head, killing her, and that he threw her body overboard, intact, in a panic.
That version of events was made public by Copenhagen City Court on September 5th.
Police said on October 7th that an autopsy of her head showed no sign of a skull injury.
The case has now been slated for a jury trial at Copenhagen City Court in the spring, Copenhagen Police also confirmed.
Eight days, spread between March 8th and April 25th 2018, have been initially set aside for the trial.
Scheduling of court proceedings was made with investigation of the case nearing completion, special prosecutor Jakob Buch-Jepsen said via the police statement.
“Naturally, there is still some investigation of relevant information to be completed, but the case is broadly ready. It will therefore now move into the presentation phase and I expect a decision to be made with regard to indictment by the end of the year,” Buch-Jepsen said.
Police divers have continued searching waters in Køge Bay over the last two weeks in an effort to locate Kim Wall’s arms as well as mobile telephones belonging to her and Madsen. That search has so far remained unsuccessful.